Answer to Question #138954 in Analytic Geometry for Cute

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 1

let c the distance between the vertex and the focus.

the equation for a vertical parabola:

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

When the center is at origin

then this equation becames

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

.

The problem gives you a point on the parabola: (10,4)

put it in and solve for 'c':

$4=\frac{1}{4c}10^2$

$c=\frac{10^2}{16}$

c $=\frac{100}{16}=6.25 feet$

So the required answer is 6.25 feet