The depth of the reflector is about feet.

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 3.5 feet above the vertex. The reflector extends 3.5 feet to either side of the vertex. What is the depth of the reflector? Round your answer to the nearest hundredth.

Answer 1

This answer to this question depends on the relation between the focus of a parabola and the equation of the parabola. For a parabola with vertex(0,0) the equation of the parabola is y = x²/4p where p is the ordinate of the focus, in this case: y=x²/14.

The depth of the reflector is the ordinate where y=3.5.

With this information, you should be able to answer the question.