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Math Help - Converting Rectanglar equation to polar equation

  1. #1
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    Converting Rectanglar equation to polar equation

    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,
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  2. #2
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    Re: Converting Rectanglar equation to polar equation

    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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