Converting Rectanglar equation to polar equation

**Cbarker1** · December 14th 2012, 05:35 PM

Dear Every one,

I need some help converting rectanglur implicit equation to polar equation:
9*(x^2+y^2)=(x^2+y^2-2y)^2. and I know the fact of r=\sqrt(x^2+y^2) and tan \theta=y/x, where x is not equal to 0.

Thank you for your help,

**Soroban** · December 14th 2012, 05:57 PM

Hello, Cbarker1!

So you know that: . $x^2 + y^2 \:=\:r^2$

Do you also know this? . $\begin{Bmatrix}x &=& r\cos\theta \\ y &=& r\sin\theta\end{Bmatrix}$

$\text{Convert to polar form: }\: 9(x^2+y^2)\:=\:(x^2+y^2-2y)^2$

What's stopping you?

$9\underbrace{(x^2+y^2)}_{r^2} \;=\;(\underbrace{x^2+y^2}_{r^2} - 2\underbrace{y}_{r\sin\theta})^2$

. . . . . $9r^2 \;=\;(r^2 - 2r\sin\theta)^2$

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