A cable TV receiving dish is the shape of a paraboloid of revolution. Find the location of the receiver, which is placed at the focus, if the dish is 7 feet across at its opening and 2.5 feet deep.

Question

How many feet above the vertex should the receiver be?

Answer 1

Sketch this as a downward opening parabola with vertex at (0, 2.5) and x-intercepts at (-3.5, 0) and (3.5, 0)

f(x) = a(x - h)² + k

f(x) = a(x - 0) + 2.5

0 = a(3.5 - 0)² + 2.5\

0 = 12.25a + 2.5

-2.5 = 12.25a

-0.204081 ≈ a

focus: (h, k + p)

p = 1 / 4a

p = -1.225

focus: (0, 2.5 - 1.225