The light from a lighthouse is often reflected from a powerful lamp using a reflector in the shape of a parabola. The parabola has the interesting property that rays from the focus are reflected parallel to the axis of the parabola.
The parabola has many interesting properties. Some of these can be investigated using the parabola equation y2 = 4ax. Others follow from the focus-directrix definition of the curve: the locus of points equi-distant from a fixed point (the focus) and a fixed line not through the point (the directrix).
Use your library to investigate this and other properties of the parabola: in particular A Book of Curves by E.H. Lockwood, C.U.P (1967).
The reflector
The light from a lighthouse is often reflected from a powerful lamp using a reflector in the shape of a parabola. The parabola has the interesting property that rays from the focus are 
The parabola has many interesting properties. Some of these can be investigated using the parabola equation y2 = 4ax. Others follow from the 