Parametric equation to cartesian calculator

# Parametric equation to cartesian calculator

I recently learned in math class how to convert the rectangular equation of a circle into a parametric equation: $x^2+y^2=1$ $\cos^2(t)+\sin^2(t)=1$Free calculus calculator - calculate limits, integrals, derivatives and series step-by-step ... Equations Inequalities Simultaneous Equations System of Inequalities Polynomials Rationales Complex Numbers Polar/Cartesian Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry ... calculus-calculator. parametric equation. en. Related ...It is often useful to have the parametric representation of a particular curve. The normal Cartesian representation (in terms of x's and y's) can be obtained by eliminating the parameter as above. Example. Find the Cartesian equation given by the parametric equations: x = at 2 (3) y = 2at (4) From (4), t = y/2a. Substituting this into (3):How do you convert the parametric equations into a Cartesian equation by eliminating the parameter r: #x=(r^2)+r#, #y=(r^2)-r#? Calculus Parametric Functions Introduction to Parametric Equations 2 AnswersCalculators. About. Help. Sign In. Sign Up. Hope that helps! You're welcome! ... Eliminate the Parameter, Step 1. Set up the parametric equation for to solve the equation for . Step 2. Rewrite the equation as . Step 3. Subtract from both sides of the equation. Step 4. Divide ... Replace in the equation for to get the equation in terms of . Step ...Graph the parametric equations x =5cost x = 5 cos t and y= 2sint y = 2 sin t. First, construct the graph using data points generated from the parametric form. Then graph the rectangular form of the equation. Compare the two graphs. Show Solution. t t. x = 5 cos t x = 5 cos ⁡ t. y = 2 sin t y = 2 sin ⁡ t. 0 0.5 (x2+y2) = y. 5×2+ 5y2-y =0. 5×2+y (5y-1)= 0. Your equation is now converted to a Cartesian equation. Another quick method is using the polar to Cartesian equation calculator. This one requires you to simply key in the polar components and get the results in the form of xs and ys. It is that simple.Parametric Equations and Polar Coordinates. Eliminate the Parameter, Step 1. Set up the parametric equation for to solve the equation for . Step 2. Rewrite the equation as . Step 3. Take the specified root of both sides of the equation to eliminate the exponent on the left side. Step 4.Embed this widget ». Added Aug 1, 2010 by astronomysoldier in Mathematics. Parametric equation solver and plotter. Send feedback | Visit Wolfram|Alpha. solve y=. and x=. Submit. Get the free "Parametric equation solver and plotter" widget for your website, blog, Wordpress, Blogger, or iGoogle.x = 3cos (t) , y = 3sin(t) Set up the parametric equation for x(t) to solve the equation for t. x = 3cos(t) Rewrite the equation as 3cos(t) = x. 3cos(t) = x. Divide each term in 3cos(t) = x by 3 and simplify. Tap for more steps... cos(t) = x 3. Take the inverse cosine of both sides of the equation to extract t from inside the cosine.Aug 27, 2021 · Graphing parametric equations on the Desmos Graphing Calculator is as easy as plotting an ordered pair. Instead of numerical coordinates, use expressions in terms of t, like (cos t, sin t ). Graph lines, curves, and relations with ease. Whether you’re interested in form, function, or both, you’ll love how Desmos handles parametric equations. The process of turning a system of parametric equations into a system of implicit equations is called implicitization. See §3.3 § 3.3 of Cox, Little, and O'Shea's Ideals, Varieties, and Algorithms for more on this. Let u = cos(t) u = cos ( t) and v = sin(t) v = sin ( t). Using de Moivre's formula, we have.Free Cartesian to Polar calculator - convert cartesian coordinates to polar step by step Consider the parametric equations below. x = t2, y = t7. (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. (b) Eliminate the parameter to find a Cartesian equation of the curve. Show transcribed image text.How do you convert the parametric equations into a Cartesian equation by eliminating the parameter r: #x=(r^2)+r#, #y=(r^2)-r#? Calculus Parametric Functions Introduction to Parametric Equations 2 Answers3d Line Calculator. This tool calculates 3d line equations : parametric, cartesian and vector equations. It works also as a line equation converter. Share calculation and page on.Free calculus calculator - calculate limits, integrals ... Equations Inequalities Simultaneous Equations System of Inequalities Polynomials Rationales Complex Numbers Polar/Cartesian Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry ... calculus-calculator. parametric equation. en. Related Symbolab blog posts. Advanced …I'm supposed to find the point of intersection between the cartesian equation and its normal to the curve at the point where the curve meets the x-axis $\endgroup$ – hohner Sep 29, 2014 at 18:05Our equation of a sphere calculator will help you write the equation of a sphere in the standard form or expanded form if you know the center and radius of the sphere. Alternatively, you can find the sphere equation if you know its center and any point on its surface or if you know the end-points of any of its diameters.This calculator can also find the center and radius of a sphere from its ...Knowing this and the fact that the particle is moving along parametric functions (as given in the problem), let's look at the corresponding arc length formula for 0 ≤ t ≤ 2: We are given dx/dt, and we can find dy/dt by finding the slope of the line segments in the graph. Between 0 and 2, there are two different line segments.2. First, evaluate x 2 ( 1 − x 2) with x = cos ( t) and verify that you get y 2. This will prove that every point in the parametric curve lies on the curve y 2 = x 2 ( 1 − x 2). But this is not enough; this only shows that the parametric curve is contained inside the curve y 2 = x 2 ( 1 − x 2). To show that the paramatric curve is the ...Polar Co-ordinatesPolar to Cartesian coordinatesCartesian to Polar coordinatesExample 3Graphing Equations in Polar CoordinatesExample 5Example 5Example 5Example 6Example 6Using SymmetryUsing SymmetryUsing SymmetryExample (Symmetry)CirclesTangents to Polar CurvesTangents to Polar CurvesExample 9The vector equation of a line is r → = 3 i ^ + 2 j ^ + k ^ + λ (i ^ + 9 j ^ + 7 k ^) ‍ , where λ ‍ is a parameter. Find the cartesian equation of this line. Choose 1 answer:In this video, I show you how to convert a parametric equation into Cartesian form. Converting trig types to Cartesian form In this video, I show you how to convert trigonometric parametric equation into Cartesian form.Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. b. First, square both sides of the equation. This gives $$r^2=9.$$ Next replace $$r^2$$ with $$x^2+y^2$$. This gives the equation $$x^2+y^2=9$$, which is the equation of a circle centered at the origin with radius 3. In general, any polar equation of the form $$r=k$$ where k is a positive constant represents a circle of radius k centered at the ...12 Mei 2020 ... (3 points) A. The parametric equations are easier to enter into a calculator for graphing. B. The parametric equations show the direction in ...A Parametric Equation Calculator is an online calculator that can solve your parametric equation problems inside your browser without any pre-requisites. This Calculator is a standard calculator with not a lot of complex processing going on. This calculator can solve the set of 2-dimensional parametric equations for multiple different inputs of ...The Formula of a ROTATED Ellipse is: $$\dfrac {((X-C_x)\cos(\theta)+(Y-C_y)\sin(\theta))^2}{(R_x)^2}+\dfrac{((X-C_x) \sin(\theta)-(Y-C_y) \cos(\theta))^2}{(R_y)^2}=1$$I know how to find the two points of intersection by converting the parametric equations to Cartesian equations of the two parabolas C1: y =f1(x) C 1: y = f 1 ( x) and C2: y =f2(x) C 2: y = f 2 ( x) by solving for x x the equation f1(x) = f2(x) f 1 ( x) = f 2 ( x). My question is about the possibility of finding the intersection points of the ...x = (v0cosθ)t y = − 1 2gt2 + (v0sinθ)t + h. where g accounts for the effects of gravity and h is the initial height of the object. Depending on the units involved in the problem, use g = 32ft/s2 or g = 9.8m/s2. The equation for x gives horizontal distance, and the equation for y gives the vertical distance.Our pair of parametric equations is. x(t) = t y(t) = 1 − t2. To graph the equations, first we construct a table of values like that in Table 10.6.2. We can choose values around t = 0, from t = − 3 to t = 3. The values in the x(t) column will be the same as those in the t column because x(t) = t.🔶 Aʙᴏᴜᴛ Tʜɪs Vɪᴅᴇᴏ – This video looks at using both Graph and Table mode to help support answering a question involving parametric equations. By switching Derivative on on the Casio fx-CG50 and tracing a graph you can discover the gradient of the curve at given values of the parameter t.The graph of parametric equations is called a parametric curve or plane curve, and is denoted by C. Notice in this definition that x and y are used in two ways. The first is as functions of the independent variable t. As t varies over the interval I, the functions x(t) and y(t) generate a set of ordered pairs (x, y).Find 100's more videos linked to the Australia Senior Maths Curriculum at http://mathsvideosaustralia.com/There are videos for:Queensland: General Mathematic...Convert parametric to cartesian. x = t sin t + cos t, y = sin t − t cos t x = t sin t + cos t, y = sin t − t cos t. to cartesian, but i'm not finding a way to get rid of t. I tried to square it all and add them up but i got x2 +y2 = t2 + 1 x 2 + y 2 = t 2 + 1. t is still there. Any tips would be amazing. thanks in advance.Table of Contents. What Is A Cartesian Equation? Cartesian Equation Calculator; Converting Polar To Cartesian Equations; Converting Parametric Equations to ...Given a parametric curve where our function is defined by two equations, one for x and one for y, and both of them in terms of a parameter t, like x=f (t) and y=g (t), we can eliminate the parameter value in a few different ways.Oct 4, 2016 · A line would be the system of two such equations (i.e. the intersection of two planes), a form you can get from the (blue) standard form by explicitly writing it as a system of two equations; e.g. $$\left\{ \begin{array}{rcl} \frac{x-a_1}{v_1} = \frac{y-a_2}{v_2} \\ \frac{y-a_2}{v_2} = \frac{z-a_3}{v_3} \end{array} \right.$$ $\endgroup$ Parametric to Cartesian. solve y =. and x =. for. Submit. Added Nov 29, 2017 by bry_perk in Mathematics. Converts a parametric equation into a Cartesian equation based on the given inputs. Summary. To convert from Polar Coordinates (r, θ) to Cartesian Coordinates (x,y) : x = r × cos ( θ ) y = r × sin ( θ ) To convert from Cartesian Coordinates (x,y) to Polar Coordinates (r,θ): r = √ ( x2 + y2 ) θ = tan-1 ( y / x ) The value of tan-1( y/x ) may need to be adjusted: Quadrant I: Use the calculator value.R(φ) =I + sin φW + 2sin2 φ 2 W2 R ( φ) = I + sin φ W + 2 sin 2 φ 2 W 2. Thus, to assemble the parametric equations for your circle: pick any point in your plane whose distance from the origin is equal to the radius of your circle, and then apply the Rodrigues rotation formula to that point.Equations Inequalities Simultaneous Equations System of Inequalities Polynomials Rationales Complex Numbers Polar/Cartesian Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry. ... cartesian-calculator. cartesian. en. Related Symbolab blog posts. Practice Makes Perfect.9.1 Defining and Differentiating Parametric Equations. Parametric functions are a way to express a relationship between variables in the form of an equation that involves time. We will often use parametric functions to express the position of an object moving in space, or to describe the shape of a curve.Converting parametric equation to Cartesian. 1. How to convert $\iint f_{xyz}(x,y,z)\,dy\,dz$ to polar coordinates? Hot Network Questions Colouring a rug Horror movie where girls are held captive by a man who is white, in good shape, and can crawl on ceilings and walls CorrelationTest vs PearsonCorrelationTest ...Equations Inequalities Simultaneous Equations System of Inequalities Polynomials Rationales Complex Numbers Polar/Cartesian Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic ... Simultaneous Equations Calculator. Solving simultaneous equations is one small algebra step further on from simple equations .... A Level Maths revision tutorial video.For the full list of videos and more revision resources visit www.mathsgenie.co.uk.Given a parametric curve where our function is defined by two equations, one for x and one for y, and both of them in terms of a parameter t, like x=f (t) and y=g (t), we can eliminate the parameter value in a few different ways.Definition 45 Parametric Equations and Curves. Let $$f$$ and $$g$$ be continuous functions on an interval $$I$$. The set of all points $$\big(x,y\big) = \big(f(t),g(t)\big)$$ in the Cartesian plane, as $$t$$ varies …Our pair of parametric equations is. x(t) = t y(t) = 1 − t2. To graph the equations, first we construct a table of values like that in Table 10.6.2. We can choose values around t = 0, from t = − 3 to t = 3. The values in the x(t) column will be the same as those in the t column because x(t) = t.Page 17 Q3, 4 and 5Page 13 Q 4 and 5Get the free "parametric to cartesian" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha.Find in scalar parametric form an equation for the line of intersection of the plane $P$ and the plane with Cartesian equation $2x + y − z = 0$. $P= x − 2y + z = 1$.Step 2 Now, you can enter the equations in their respective input boxes which are labeled as: solve y and x. We now define and as and and get the parametric form as: First, set up the input parametric equations properly, which means keeping the parameter the same. We solve the cartesian form for one variable, for example : We are given a plane ...This video explains how to write parametric equations as a Cartesian or rectangular equation. Site: http://mathispower4u.comBlog: http://mathispower4u.wor...Cartesian Equation from Parametric Equations. Consider the equations above x = 1 / t, y = 2 t for 0 < t ≤ 5. We can find the Cartesian equation by eliminating t. We rearrange the x equation to get t = 1 x and substituting gives y = 2 x . Note that the t values are limited and so will the x and y values be in the Cartesian equation.October 3, 2023 by GEGCalculators. To convert a parametric equation to a Cartesian equation, express one variable in terms of the other (s) using the parameter as needed. Eliminate the parameter (s) to obtain a single equation involving only the Cartesian coordinates, typically x and y in two dimensions, or x, y, and z in three dimensions.Plot the solution to an equation in two variables: plot 3x^2-2xy+y^2=1. Plot a quadric surface: ... Draw a parametric curve in three dimensions: 3d parametric plot ...A sketch of the parametric curve (including direction of motion) based on the equation you get by eliminating the parameter. Limits on x x and y y. A range of t t 's for a single trace of the parametric curve. The number of traces of the curve the particle makes if an overall range of t t 's is provided in the problem.6 Jul 2012 ... This video explains how to write parametric equations as a Cartesian or rectangular equation ... Graphing Calculator (199); XIII. Other (434); XIV ...Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.The idea of utilizing parametric equations is to permit to plot a curve through the continuos variation of a variable named 'parameter' without the danger of obtaining ambiguos or imaginary values. Example : The cartesian function of a circle : X^2 + Y^2 = R^2 permits to solve for Y: Y = + -sqrt(R^2 - X^2)x = a cos ty = b sin t. t is the parameter, which ranges from 0 to 2π radians. This equation is very similar to the one used to define a circle, and much of the discussion is omitted here to avoid duplication. See Parametric equation of a circle as an introduction to this topic. The only difference between the circle and the ellipse is that in ...Tutorial on parametric equations and converting to cartesian form.YOUTUBE CHANNEL at https://www.youtube.com/ExamSolutionsEXAMSOLUTIONS WEBSITE at https://ww...Set up the parametric equation for to solve the equation for . Step 2. Rewrite the equation as . Step 3. In this video we derive a parametric vector form for a plane in 3D in two different ways: visually and using some algebra. This is Chapter 1, Problem 41 d) o...The framework of these calculators are built on the symbolic structure, the vast algorithms that have been created and lastly many ideas from NKS (new kind of science) Use this calculator for your personal endeavors that may require such calculations. The calculator provides accurate calculations after submission. Free calculus calculator - calculate limits, integrals, derivatives and series step-by-step ... Equations Inequalities Simultaneous Equations System of Inequalities Polynomials Rationales Complex Numbers Polar/Cartesian Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry ... calculus-calculator. parametric equation. en. Related ...Methods for Finding Cartesian and Polar Equations from Curves. In many cases, we may have a pair of parametric equations but find that it is simpler to draw a curve if the equation involves only two variables, such as $x$ and $y$. Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this siteI've been trying to find the formula for the offset/parallel to a sine wave. Not just the parametric equation, but the y = f(x) form. Here's what I've done so far: Read up on the parametric form and plugged in the x(t) and y(t) formulas. What I get is of course a parametric equation in terms of t. If $$y=\sin(x)$$For problems 12 - 14 write down a set of parametric equations for the given equation that meets the given extra conditions (if any). y = 3x2−ln(4x +2) y = 3 x 2 − ln. ⁡. ( 4 x + 2) Solution. x2 +y2 = 36 x 2 + y 2 = 36 and the parametric curve resulting from the parametric equations should be at (6,0) ( 6, 0) when t = 0 t = 0 and the ...8.6 Parametric Equations; 8.7 Parametric Equations: Graphs; 8.8 Vectors; Chapter Review. Key Terms; Key Equations; ... we need to enter the positive and negative square roots into the calculator separately, as two equations in the form Y 1 = 9 ... convert the given Cartesian equation to a polar equation. 16. x = 3 x = 3. 17. y = 4 y = 4. 18. y ...Solution We plot the graphs of parametric equations in much the same manner as we plotted graphs of functions like y = f ... Solution We again start by making a table of values in Figure 10.2.2 (a), then plot the points (x, y) on the Cartesian plane in Figure 10.2.2 (b). The curves in Examples 10.2.1 and 10.2.2 are portions of the same parabola ...1. Equation of normal at (a cos t, b sin t) ( a cos t, b sin t) is: ax sec t − by csc t = a2 −b2 a x sec t − b y csc t = a 2 − b 2. The x, y x, y -intercepts are a2−b2 a cos t a 2 − b 2 a cos t and a2−b2 b sin t a 2 − b 2 b sin t respectively. Hence the locus is.Assuming "parametric equations" is a general topic | Use as referring to a mathematical definition instead. Examples for Plotting & Graphics. Functions. Plot a function of one variable: plot x^3 - 6x^2 + 4x + 12. graph sin t + cos (sqrt(3)t) plot 4/(9*x^(1/4)) Specify an explicit range for the variable:Equations Inequalities Simultaneous Equations System of Inequalities Polynomials Rationales Complex Numbers Polar/Cartesian Functions Arithmetic & Comp. Coordinate …Set up the parametric equation for to solve the equation for . Step 2. Rewrite the equation as . Step 3. Divide each term in by and simplify. Tap for more steps... Step 3.1. Divide ... Take the inverse cosine of both sides of the equation to extract from inside the cosine. Step 5. Replace in the equation for to get the equation in terms of ...The graph does not represent a function, as it will fail the vertical line test. The graph is drawn in two parts: the positive values for t t, and the negative values for t t. Exercise 10.7.1 10.7. 1. Sketch the graph of the parametric equations x = t√ x = t, y = 2t + 3 y = 2 t + 3, 0 ≤ t ≤ 3 0 ≤ t ≤ 3. Answer.parametric to cartesian. Computing... Get the free "parametric to cartesian" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha. Set up the parametric equation for x(t) x ( t) to solve the equation for t t. Rewrite the equation as t+ 1 t = x t + 1 t = x. Find the LCD of the terms in the equation. Tap for more steps... Multiply each term in t+ 1 t = x t + 1 t = x by t t to eliminate the fractions.Completing the square method is a technique for find the solutions of a quadratic equation of the form ax^2 + bx + c = 0. This method involves completing the square of the quadratic expression to the form (x + d)^2 = e, where d and e are constants.I recently learned in math class how to convert the rectangular equation of a circle into a parametric equation: $x^2+y^2=1$ $\cos^2(t)+\sin^2(t)=1$Apr 27, 2023 · An object travels at a steady rate along a straight path $$(−5, 3)$$ to $$(3, −1)$$ in the same plane in four seconds. The coordinates are measured in meters. Find parametric equations for the position of the object. Solution. The parametric equations are simple linear expressions, but we need to view this problem in a step-by-step fashion. Expert Answer. 100% (3 ratings) Transcribed image text: Write the parametric equations in the given Cartesian form. Write the parametric equations as a function of z in Cartesian form. 1 witha0. Write the parametric equations in the given Catesian form. with 0 < x < 4. Write the parametric equations x=2sin θ, y=2cos θ, 0<θ<π in the given ...Then one parametric form is $(\frac{12+3s-6t}{4},s,t)$. In the general case of a set of linear equations, it helps thinking of the equations that need parametrization as a system with more variables than equations. The key is to find how many secondary variables are there, and take them as parameters.There are more than just one (1) possible solution to the given equation but to demonstrate how to derive at one solution I have prepared the following solution with the help of a soon-to-be PhD friend. I'm excited to see other people provide their answers to other possible equations that satisfy the original equation!Follow these steps to change the mode of your calculator: Press [MODE] and put the calculator in Parametric mode. To highlight an item in the Mode menu, use the arrow keys to place the cursor on the item, and then press [ENTER]. Highlight PARAMETRIC in the fifth line to put the calculator in Parametric mode. See the first …Set up the parametric equation for x(t) to solve the equation for t. x = 2− 3t Rewrite the equation as 2−3t = x. 2−3t = x Subtract 2 from both sides of the equation. −3t = x−2 Divide each term in −3t = x−2 by −3 and simplify. Tap for more steps... t = − x 3 + 2 3 Replace t in the equation for y to get the equation in terms of x. y = 5− x 3 + 2 3Then one parametric form is $(\frac{12+3s-6t}{4},s,t)$. In the general case of a set of linear equations, it helps thinking of the equations that need parametrization as a system with more variables than equations. The key is to find how many secondary variables are there, and take them as parameters.I'm supposed to find the point of intersection between the cartesian equation and its normal to the curve at the point where the curve meets the x-axis $\endgroup$ – hohner Sep 29, 2014 at 18:05The parametric equation consists of one point (written as a vector) and two directions of the plane. The point-normal form consists of a point and a normal vector standing perpendicular to the plane. The coordinate form is an equation that gives connections between all the coordinates of points of that plane?These equations are called the implicit equations for the line: the line is defined implicitly as the simultaneous solutions to those two equations. The parametric form. E x = 1 − 5 z y = − 1 − 2 z . can be written as follows: ( x , y , z )= ( 1 − 5 z , − 1 − 2 z , z ) z anyrealnumber. This called a parameterized equation for the ...Figure 7.2 depicts Earth’s orbit around the Sun during one year. The point labeled F 2 F 2 is one of the foci of the ellipse; the other focus is occupied by the Sun. If we superimpose coordinate axes over this graph, then we can assign ordered pairs to each point on the ellipse ().Then each x value on the graph is a value of position as a function of time, and …However, there are various methods we can use to rewrite a set of parametric equations as a Cartesian equation. The simplest method is to set one equation equal to the parameter, such as $\,x\left (t\right)=t.\,$In this case, $\,y\left (t\right)\,$can be any expression. For example, consider the following pair of ...Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this siteEquations Inequalities Simultaneous Equations System of Inequalities Polynomials Rationales Complex Numbers Polar/Cartesian Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry. ... linear-algebra-calculator. en. Related Symbolab blog posts. The Matrix, Inverse ...Finding Cartesian equations from parametric equations. 0. Parametric equations of manifold. 2. Find the cartesian equation from the given parametric equations. 0. Converting parametric equations with trigonometric functions into Cartesian form. 1.Set up the parametric equation for to solve the equation for . Step 2. Rewrite the equation as . Step 3.To convert parametric equations to rectangular form, express x and y in terms of a parameter (typically denoted as t), then eliminate t. For example, for parametric equations x = 2t and y = t^2, we can eliminate t by solving for t in the first equation (t = x/2) and substituting it into the second equation (y = (x/2)^2).High School Math Solutions – Systems of Equations Calculator, Elimination. A system of equations is a collection of two or more equations with the same set of variables. In this blog post,... Read More. Save to Notebook! Sign in. Free Sets Caretesian Product Calculator - Find the caretesian product of two sets step-by-step.May 18, 2017 · How do you convert the parametric equations into a Cartesian equation by eliminating the parameter r: #x=(r^2)+r#, #y=(r^2)-r#? Calculus Parametric Functions Introduction to Parametric Equations 2 Answers x=y^2/16 We know that x=4t^2 and y=8t. We're going to eliminate the parameter t from the equations. Since y=8t we know that t=y/8. We can now substitute for t in x=4t^2: x=4(y/8)^2\\rightarrow x=(4y^2)/64\\rightarrow x=y^2/16 Although it is not a function, x=y^2/16 is a form of the Cartesian equation of the curve. It's frequently the case that you do not end up with y as a function of x when ...