How do you convert $2y= -x^2-2x$ into a polar equation?

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Answer 1 · 2017-12-01T13:05:10

$2sintheta+rcos^2theta+2costheta=0$

Using the fact that:

$x=rcostheta$ and $y=rsintheta$

We can substitute these into the equation:

$2y=-x^2-2x$

$2(rsintheta)=-(rcostheta)^2-2(rcostheta)$

$2rsintheta=-r^2cos^2theta-2rcostheta$

$2sintheta=-rcos^2theta-2costheta$

$2sintheta+rcos^2theta+2costheta=0$

How do you convert 2y= -x^2-2x 2y= -x^2-2x into a polar equation?