Question

Transform the polar equation r2= a2cos2θ into cartensian form.

Answer 1

The given equation is

     r2 = a2 cos2θ  

or r2 = a2 (cos2θ - sin2θ) , ( so, cos2θ = cos2θ - sin2θ)

Putting cosθ = x/r, sinθ = y/r and r =√(X2 + y2) , we get

or r2(x2+y2) = a2(x2_y2)

or (X2+y2)(X2+y2) = a2(x2-y2)

or (X2+y2) = a2(x2_y2)

This is the required equation in cartesian form.