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

Salvador Bush

17 March, 05:09

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.

+3

Answers (1)

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Noemi Hutchinson · 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