shadow cast by a circle

Question

A point source emits light at a circular disc (thickness negligible), and a shadow is left on a wall (XY plane) behind and parallel to the disc. The Z component of distance between the point source and the disc is 'a' units. The Z component of distance between disc and wall is 'b' units. The line joining the point source and the centre of the disc lies on the YZ plane, intersects the wall (XY plane) at origin, and intersects the Z axis at angle theta. If the radius of the disc is r, find the equation of the perimeter of the shadow projected on the XY plane

Answer 1

I think you can use similar triangles to show that the image is a circle centred at the origin and calculate the radius. Take a point $P$ on the circle. Call the position of the light source $S$, the centre of the circle $C$, the origin $O$ and let the image of $P$ in the $XY$ plane be $Q$.

Then $CP$ is parallel to $OQ$ because the circle lies in a plane parallel to the $XY$ plane, so $\triangle SOQ$ is similar to $\triangle SCP$. The similarity ratio is $\frac {SO}{SC}$ and the distance $OQ = r\frac {SO}{SC}$.