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#