Answer to Question #144549 in Analytic Geometry for Keana

Question

A satellite dish in the shape of 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 1

Let c denote the distance between the focus and the vertex.

The equation for a vertical parabola:

$y = \frac{1}{4c}(x-h)^2+k$

Considering the parabola with center at (0, 0):

$y = \frac{1}{4c}x^2$

Now it is given that the dish is 10ft across and 4ft deep at its vertex, this gives a point on the parabola (10, 4):

$4 = \frac{1}{4c}\cdot10^2$$\implies$ $c=\frac{100}{16}=6.25$

Answer: 6.25ft.