Equation of the line touching both parabolas $y^2=4 x$ and $x^2=-32 y$ is

If the normal chord drawn at $(2 a, 2 a \sqrt{2})$ on the parabola $y^2=4 a x$ subtends an angle $\theta$ at its vertex, then $\theta=$

If the ordinates of points $P$ and $Q$ on the parabola $y^2=12 x$ are in the ratio $1: 2$. Then, the locus of the point of intersection of the normals to the parabola at $P$ and $Q$ is

A common tangent to the circle $x^2+y^2=9$ and parabola $y^2=8 x$ is