I'm trying to convert the rectangular cartesian equation
$$
y^2 = 4(x + 1)
$$
to a polar equation. After replacing $y = r \sin \theta$ and $x = r \cos \theta$, I get
$$
r^2 \sin^2 \theta = 4(r \cos \theta + 1)
$$
After replacing $\sin^2 \theta = 1 – \cos^2 \theta$ and rearranging, I get
$$
r^2 – r^2 \cos^2 \theta – 4r \cos \theta -4 = 0
$$
That's where I'm stuck and I can't solve the equation in terms of $r$.
Best Answer
Basic approach. Rewrite your equation as
$$ (\sin^2\theta) r^2 - (4\cos\theta) r - 4 = 0 $$
and use the quadratic formula for $r$.