# Thread: Parametric equations.

1. ## Parametric equations.

<Any Help would be greatly appreciated>
This stuff confuses me

6. Elimante the parameter and write the corresponding rectangular equation adjustin the domain as necessary for the parametric equations x=2cosø and y=3sinø.

7. Find a set of parametric equations for the rectangular equation x=3y-2 by using:
A) x=t
B) 2-x=t

2. Hello, jrose011!

Here's #6 . . .

6. Eliminate the parameter: . $\begin{array}{c}x \:=\:2\cos\theta \\ y \:=\:3\sin\theta \end{array}$
We have the equations: . $\begin{array}{c}\dfrac{x}{2} \:=\:\cos\theta \\ \\[-3mm] \dfrac{y}{3} \:=\:\sin\theta \end{array}$

Square the equations: . $\begin{array}{cc}\dfrac{x^2}{4} \:=\:\cos^2\!\theta & {\color{blue}[1]} \\ \\[-3mm] \dfrac{y^2}{9} \:=\:\sin^2\!\theta & {\color{blue}[2]} \end{array}$

$\text{Add {\color{blue}[1]} and {\color{blue}[2]}: }\;\frac{x^2}{4} + \frac{y^2}{9} \;=\;\underbrace{\cos^2\!\theta + \sin^2\!\theta}_{\text{This is 1}}$

. . Therefore: . $\frac{x^2}{4} + \frac{y^2}{9} \;=\;1 \quad\hdots\;\text{ an ellipse}$

3. Thanks alot! Really helped and makes perfect sense.