# Equation describing the shape of a concave mirror

What is the equation describing the shape of a mirror with the property that light rays from a point source placed at the origin will be reflected in a beam of rays parallel to the x-axis?

From the Wikipedia page I can quote that the relation is $4 f y = x^2$ where $f$ is the distance of the focus to the origin of the parabola.
Your focus is at $(a, 0)$, so the equation would be $4 a x = y^2$. You can solve that equation for $y$ and have a function $y = f(x) = \sqrt{4 a x}$.