You are designing a lamp reflector for a spotlight.

Question

You are designing a lamp reflector for a spotlight. If you want to placc the lamp 50cm from the vertex of the parabolic reflector, find the equation of the parabola that describes the shape of the reflector.

Answer 1

We can write the general equation of a parabola as y = 1/(4p)(x - h)² + k where the vertex is at the point (h, k) and the focus is a distance of "p" units from the vertex.

Placing the lamp 50 cm from the vertex means p = 50. If we assume the vertex is at the point (0, 0) in other words we set our coordinate system up at the vertex, then the equation of the parabola can be:

y = 1/(4•50)(x - 0)² + 0

or y = (1/200)x²

You could also write this equation as 200y = x²