# 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.

solution here

## 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 $$C$$.

solution here