The original question asked to
Prove that the perpendicular focal chord of a rectangular hyperbola are equal.
For finding the length of the focal chords of a hyperbola, how to use polar /parametric form ??
For it, what I did was use a parametric form so I found the equation of a point as $(ae + r\cos\theta,r \sin \theta)$, then I would put the point in the corresponding equation of the hyperbola $ \frac{x^2}{a^2}-\frac{y^2}{b^2} = 1$ , so I will get a quadratic in $r$.
Let its root be $r_1, r_2$. Since they are on different sides, one will be positive, the other negative. Let $r_1> 0, r_2<0$
I am already provided with $\theta$ in the question.
Now my question is, for the length, would I need to take the sum of the roots or their difference??