Question

The cross section of a parabolic reflector has a vertical axis of symmetry with its vertex at (0,0). The focus of the reflector is 6 feet above the vertex. The reflector extends 5.5 feet to either side of the vertex. What is the depth of the reflector? Round your answer to the nearest hundredth.

The depth of the reflector is about _____

feet.

Answer 1

1.26 feets

Explanation:

Given the following :

Vertex (0, 0)

Focus of reflector = 6 feets

Extension = 5.5 feets

Equation to obtain conic section of a parabola:

(x - h)² = 4p(y - k)

Vertex (0, 0)

h =0 ; k = 0, p = 6, x = 5.5

(5.5 - 0)² = 4*6(y - 0)

30.25 - 0 = 24(y - 0)

30.25 = 24y

y = 30.25 / 24

y = 1.26

Hence, depth of reflector = 1.26 feets