Write as:
y^2 - 4x^2 - 2y - 2x = 0y2−4x2−2y−2x=0
Substitute rsin(theta)rsin(θ) for every y and rcos(theta)rcos(θ) for every x:
(rsin(theta))^2 - 4(rcos(theta))^2 - 2(rsin(theta)) - 2(rcos(theta)) = 0(rsin(θ))2−4(rcos(θ))2−2(rsin(θ))−2(rcos(θ))=0
Put common factors outside of the ()s:
(sin^2(theta) - 4cos^2(theta))r^2 - 2r(sin(theta) - cos(theta)) = 0(sin2(θ)−4cos2(θ))r2−2r(sin(θ)−cos(θ))=0
Most the second term to the right:
(sin^2(theta) - 4cos^2(theta))r^2 = 2r(sin(theta) - cos(theta))(sin2(θ)−4cos2(θ))r2=2r(sin(θ)−cos(θ))
Divide both sides by (sin^2(theta) - 4cos^2(theta))r(sin2(θ)−4cos2(θ))r
r = 2(sin(theta) - cos(theta))/(sin^2(theta) - 4cos^2(theta))r=2sin(θ)−cos(θ)sin2(θ)−4cos2(θ)
