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 is the receiver?

Answer 1

The distance sought is "p", the distance from the vertex to the focus.

p = 1 / 4a, where "a" is the coefficient in f(x) = a(x - h)² + k

Draw an cross section of the parabolic disc. With the vertex at (0, 2.5) and x-intercepts at (-3.5, 0) and (3.5, 0).

0 = a(3.5)² + 2.5

0 = 12.25a + 2.5

-2.5 = 12.25a

-0.204081 ≈ a

p = -1.225

The focus should be 1.225 ft from the vertex.