Conic Sections and Parametric Equations · Superchallenge problem

The point $A=(2,0)$ is a vertex of the ellipse $\dfrac{x^2}{4}+y^2=1$. Points $P$ and $Q$ are on the ellipse, different from $A$, with $\angle PAQ=90^\circ$. As $P$ and $Q$ vary, the line $PQ$ always passes through one fixed point. Find the $x$-coordinate of that point.