Answer
The graph of $4x^2+9y^2-36y=0$
Parametric equations:
$x=3~cos~t$
$y=2+2~sin~t$
Work Step by Step
If you can not insert the function into your graphics device as shown, do the following:
$4x^2+9y^2-36y=0$
$4x^2+9y^2-36y+36=36$
$4x^2+9(y^2-4y+4)=36$
$4x^2+9(y-2)^2=36$
$\frac{x^2}{9}+\frac{(y-2)^2}{4}=1$
$(\frac{x}{3})^2+(\frac{y-2}{2})^2=1$
Now, use parametric equations:
Make:
$\frac{x}{3}=cos~t$
$x=3~cos~t$
$\frac{y-2}{2}=sin~t$
$y-2=2~sin~t$
$y=2+2~sin~t$
Remember: $cos^2t+sin^2t=1$
