From a point $P(h,k)$, two tangents are drawn to the parabola $y^2 = 4ax$ which are perpendicular to each other. Find the locus of $P$.
The two points of tangency are $(at^2, 2at)$ and $(at^2, -2at)$ (since $s = -t$). Equal distances from $P$ give $k = 0$. The locus of $P$ is $y = 0$, a straight line. (D)
From a point $P(h,k)$, two tangents are drawn to the parabola $y^2 = 4ax$ which are perpendicular to each other. Find the locus of $P$.