How do you convert $r^2=cos2 theta$ to rectangular form?

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Answer 1 · 2016-09-27T08:05:08

We know the relations

$x=rcostheta and y =rsintheta$

where r and $theta$ are the polar coordinate of a point having rectangular coordinate $(x,y)$
So $r^2=x^2+y^2$

Now the given relation is

$r^2=cos2theta=cos^2theta-sin^2theta$

$=>r^4=r^2cos^2theta-r^2sin^2theta$

$=>(x^2+y^2)^2=x^2-y^2$

This is the rectangular form of the given polar equation.

How do you convert r^2=cos2 theta r^2=cos2 theta to rectangular form?