# Problems

## Cresent Cake Cutting

A circular cake is cut by another circle, centred on its edge. Find the ratio of the radii that results in the areas of the two pieces of cake are equal.

## Focus of Parabola

Parabolae (and spun parabolae) are used as antennae to focus the energy on a single point. Find the coordinates of the focus (the point where all vertical rays are reflected through) for parabola \(Ax^2+Bx+C\) at in terms of \(A\), \(B\) and \(C\).