Curved Mirror producing Parallel Rays is Paraboloid

Theorem
Let $M$ be a curved mirror embedded in a real cartesian $3$- space.

Let there be a source of light at the origin.

Let $M$ reflect the light in a beam parallel to the $x$-axis.

Then $M$ is the solid of revolution produced by rotating about the $x$-axis the parabola whose equation is:
 * $y^2 = 2 c x + c^2$