Question

A ceiling light has a cross-section in the shape of a parabola. The parabola is 24 cm wide and 9 cm deep. The lightbulb is located at the focus of the parabola. How far from the vertex is the lightbulb?

Answer 1

4 cm

Explanation:

The equation of a parabola with its vertex at the origin can be written as ...

y = 1/(4p)x^2

The problem statement tells us that one point on the parabola is (x, y) = (12, 9). We can put these values into the equation and solve for p, the distance from the focus to the vertex.

9 = 1/(4p)(12^2)

9×4/144 = 1/p = 1/4 . . . . . . . . multiply by the inverse of the coefficient of 1/p

Then p = 4, and the bulb is 4 cm from the vertex.