How do you convert y=y^2-2x^2 -4x y=y22x24x into a polar equation?

1 Answer
Jun 4, 2017

The polar equation is r=(sintheta+4costheta)/(sin^2theta-2cos^2theta)r=sinθ+4cosθsin2θ2cos2θ

Explanation:

To convert from rectangular coordinates (x,y)(x,y) to polar coordinates (r,theta)(r,θ), we use the following

x=rcosthetax=rcosθ

y=rsinthetay=rsinθ

Our equation is

y=y^2-2x^2-4xy=y22x24x

rsintheta=r^2sin^2theta-2r^2cos^2theta-4rcosthetarsinθ=r2sin2θ2r2cos2θ4rcosθ

Dividing by r!=0r0

sintheta=rsin^2theta-2rcos^2theta-4costhetasinθ=rsin2θ2rcos2θ4cosθ

r(sin^2theta-2cos^2theta)=sin theta+4costhetar(sin2θ2cos2θ)=sinθ+4cosθ

r=(sintheta+4costheta)/(sin^2theta-2cos^2theta)r=sinθ+4cosθsin2θ2cos2θ