We define the following variables: x = r * cos (θ) y = r * sine (θ) Substituting the variables we have: x = -y ^ 2 r * cos (θ) = - (r * sin (θ)) ^ 2 Rewriting: r * cos (θ) = - (r ^ 2 * sin ^ 2 (θ)) We cleared r: r = - ((cos (θ)) / (sin ^ 2 (θ))) We rewrite: r = - ((cos (θ)) / (sin (θ))) * (1 / sin (θ)) r = - cot (θ) * csc (θ) Answer: a polar equation of the form r = f (θ) for the curve represented by the cartesian equation x = -y2 is: r = - cot (θ) * csc (θ)
