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Parametric To Cartesian Equation Calculator + Online Solver With Free Steps

A Parametric to Cartesian Equation Calculator is an online solver that only needs two parametric equations for x and y to provide you with its Cartesian coordinates. The solution of the Parametric to Cartesian Equation is very simple.

We must take ‘t’ out of parametric equations to get a Cartesian equation. This is accomplished by making ‘t’ the subject of one of the equations for x or y and then substituting it into the other equation.

What Is a Parametric To Cartesian Equation Calculator?

The Parametric to Cartesian Equation Calculator is an online tool that is utilized as a parametric form calculator, which defines the circumferential way regarding variable t, as you change the form of the standard equation to this form.

This conversion process could seem overly complicated at first, but with the aid of a parametric equation calculator, it can be completed more quickly and simply.

You can reverse this after the function was converted into this procedure by getting rid of the calculator. You will get rid of the parameter that the parametric equation calculator uses in the elimination process.

It is sometimes referred to as the transformation process. The parameter t that is added to determine the pair or set that is used to calculate the various shapes in the parametric equation’s calculator must be eliminated or removed when converting these equations to a normal one.

To perform the elimination, you must first solve the equation x=f(t) and take it out of it using the derivation procedure. Next, you must enter the value of t into the Y. You will then discover what X and Y are worth.

The result will be a normal function with only the variables x and y, where y is dependent on the value of x that is displayed in a separate window of the parametric equation solver.

How To Use a Parametric To Cartesian Equation Calculator

You can use the Parametric to Cartesian Equation Calculator by following the given detailed guidelines, and the calculator will provide you with your desired results. Follow the given instructions to get the value of the variable for the given equation.

Step 1

Find a set of equations for the given function of any geometric shape.

Step 2

Then, set any one variable to equal the parameter t.

Step 3

Determine the value of a second variable related to variable t.

Step 4

Then you’ll obtain the set or pair of these equations.

Step 5

Fill in the provided input boxes with the equations for x and y.

Step 6

Click on the “SUBMIT” button to convert the given parametric equation into a cartesian equation and also the whole step-by-step solution for the Parametric to Cartesian Equation will be displayed.

How Does Parametric To Cartesian Equation Calculator Work?

The Parametric to Cartesian Equation Calculator works on the principle of elimination of variable t. A Cartesian equation is one that solely considers variables x and y.

We must take t out of parametric equations to get a Cartesian equation. This is accomplished by making t the subject of one of the equations for x or y and then substituting it into the other equation.

In mathematics, there are many equations and formulae that can be utilized to solve many types of mathematical issues. These equations and theorems are useful for practical purposes as well, though.

This equation is the simplest to apply and most important to grasp a notion among them. You can use online tools like a parametric equation calculator if you find it difficult to calculate equations manually.

It is necessary to understand the precise definitions of all words to use a parametric equations calculator.

This term is used to identify and describe mathematical procedures that, function, introduce and discuss additional, independent variables known as parameters.

The quantities that are defined by this equation are a collection or group of quantities that are functions of the independent variables known as parameters.

The main purpose of it is to investigate the positions of the points that define a geometric object. Look over the example below to obtain a clear understanding of this phrase and its equation.

Let’s look at a circle as an illustration of these equations. A circle is defined using the two equations below.

X = r cos (t) 
Y = r sin (t) 

The parameter t is a variable but not the actual section of the circle in the equations above.

However, the value of the X and Y value pair will be generated by parameter T and will rely on the circle radius r. Any geometric shape may be used to define these equations.

Solved Examples

Let’s explore some detailed examples to better understand the working of the Parametric to Cartesian Calculator.

Example 1

Given $x(t) = t^2+1$ and $y(t) = 2+t$, remove the parameter and write the equations as Cartesian equation.

Solution

We will start with the equation for y because the linear equation is easier to solve for t.

y = 2+t 

y  –  2 = t 

Next, substitute (y-2) for t in x(t) \[ x = t^2+1 \]

\[ x=(y-2)^2+1\]

Substitute the expression for t into x.

\[ x = y^2-4y+4+1 \]

\[ x =y^2-4y+5 \]

The Cartesian form is \[x=y^2-4y+5\]

Analysis

This is a correct equation for a parabola in which, in rectangular terms, x is dependent on y.

Example 2

Remove the parameter from the given pair of trigonometric equations were $0 \leq t \leq 2pi$

x(t)=4 cos t

y(t)= 3sin t 

Solution

Solve for cos t and sin t:

x=4 cos t 

\[\frac{x}{4}= \cos t \]

y = 3 sin t 

\[\frac{y}{3}= \sin t \]

Next, we will use the Pythagorean identity to make the substitutions.

\[ \cos^2 t + \sin^2 t = 1\]

\[(\frac{x}{4}^2)+(\frac{y}{3})^2= 1 \]

\[(\frac{x^2}{16})+(\frac{y^2}{9})= 1 \]

Analysis

Applying the general equations for conic sections shows the orientation of the curve with increasing values of t.

Example 3

Remove the parameter and write it as a Cartesian equation:

\[x(t)= \sqrt(t)+2\] \[y(t)= \log t\]

Solution

Solve the first equation for ‘t’

. \[x = \sqrt(t)+2\]

\[x – 2= \sqrt(t)\]

Taking square on both sides.

\[(x – 2)^2= t\]

Substituting the expression for t into the equation of y.

y=log t

\[ y = \log (x-2)^2 \]

The Cartesian form is $ y = \log (x-2)^2 $

Analysis

To make sure that the parametric equations are the same as the Cartesian equation, check the domains. The parametric equations restrict the domain on $x=\sqrt(t)+2$ to $t \geq 0$; we restrict the domain on x to $x \geq 2$.

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