Hi,

So let $\displaystyle P(a\cos\theta, b\sin\theta)$ and $\displaystyle Q(a\cos\phi, b\sin\phi)$ be points on the standard ellipse. I'm trying to show that if $\displaystyle PQ$ subtends a right angle at the point $\displaystyle (a, 0)$ then the chord $\displaystyle PQ$ passes through a fixed point on the x-axis.

So far I've gotten that $\displaystyle x = \frac{a\sin(\theta + \phi)}{\sin\phi - \sin\theta}$ and I need to show that this is invariant. The condition (that P - (a, 0) - Q forms a right angle) gives me

$\displaystyle b^2 \sin\theta \sin \phi = -a^2 (\cos\theta - 1)(\cos\phi - 1)$

I've messed around with this for well over 2 hours and all I've gotten into is a terrible mess with some very tedious algebra and nothing to show for it!

Any help would be

**much** appreciated, thanks

Stonehambey