Rewrite the Cartesian equation y = 4x^2 as a polar equation

Question

 = ?

Answer 1

Sub in the polar transform: y = rsin(theta) and x = rcos(theta) through the equation and solve for r in terms of theta.

Answer 2

r sin θ = 4 r² cos² θ

sin θ / cos² θ = 4r

tan θ sec θ = 4r

(0.25) tan θ sec θ = r