An engineer designs a satellite dish with a parabolic cross section. The dish is 16 ft wide at the opening, and the focus is placed 6 ft from the vertex.

a) Position a coordinate system with the origin at the vertex and the x-axis on the parabola's axis of symmetry and find an equation of the parabola.

b) Find the depth of the satellite dish at the vertex.

Question

Mathematics

Lane Irwin

8 March, 16:23

An engineer designs a satellite dish with a parabolic cross section. The dish is 16 ft wide at the opening, and the focus is placed 6 ft from the vertex.

a) Position a coordinate system with the origin at the vertex and the x-axis on the parabola's axis of symmetry and find an equation of the parabola.

b) Find the depth of the satellite dish at the vertex.

+4

Answers (1)

Know the Answer?

Avery Grimes · Answer 1

We are given

width = 16 ft

focus = 6 ft from the vertex

The equation of the parabola is

y = 4ax^2

a = 6

y = 4 (6) x^2

y = 24 x^2

The depth of the satellite dish is

y = 24 (16/2) ^2

y = 1536 ft