A satellite dish in the shape of a paraboloid is 10 ft across, and 4 ft deep at its vertex. how far is the receiver from the vertex, if it is placed at the focus? round off your answer to 2 decimal places.

Question: A satellite dish in the shape of a paraboloid is 10 ft across, and 4 ft deep at its vertex. How far is the receiver from the vertex, if it is placed at the focus? Round off your answer to 2 decimal places.

Answer: You are trying to find ‘c’ — the distance between the vertex and the focus.
Think of the equation for a vertical parabola:

y = (1/4c)(x-h)^2 + k

If we place our parabola at the center our equation becomes:
y = (1/4c)x^2

.

The problem gives you a point on the parabola: (10,4)
Plug it in and solve for ‘c’:

y = (1/4c)x^2
4 = (1/4c)10^2
4 = (1/4c)100
4 = (1/c)25
4c = 25
c = 25/4

c = 6.25 feet