Question 127
Let $F$ be a point, $d$ be a line, and let $\mathcal{P}$ be the parabola with focus $F$ and directrix $d$, i.e. the set of points which are equidistant from $F$ and $d$. Show that there is a line $\ell$ such that for any point $A$ on $\mathcal{P}$, the circle with diameter $A F$ is tangent to $\ell$.