Consider a curve given in polar coordinates by $r(θ)=\frac{1}{1+e\cos\theta}$, where $e≥0$.
When $e>1$, show that the curve approaches two asymptotes, find them and sketch the curve. Hint: If the critical angles are $\pm\theta_0$, compute the vertical distance of the point of the curve at angle $\theta=θ_0+h$ to the line $θ=θ_0$, and take a limit using Taylor approximations.
Not really sure where to begin, I could get $y=\frac{\sin(\theta_0+h)}{1+e\cos(\theta_0+h)}$ and $y=(\tan\theta_0)x$ and then distance is $$\frac{\sin(\theta_0+h)}{1+e\cos(\theta_0+h)}-(\tan\theta_0)x$$
is this where I'm supposed to take limits?