Find the equation of the parabola. How far above the vertex should the receiver be placed? Select an answer inches Hz cm feet dB

Question

A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is 80 feet across at its opening and 5 feet deep at its center, where should the receiver be placed?

nasa.gov

Find the equation of the parabola.   

How far above the vertex should the receiver be placed?  Select an answer inches Hz cm feet dB 

Answer 1

If parabola is open up, the equation form we need is:

x² =4py

Where:

(0,0) = vertex

p= distance from vertex to focus (which is what we are looking for.)

(x,y)= a point in parabola.

One of the points is (40,5):

40² =4p(5)

1600 = 20p

p= 1600/20 = 80 ft.

Therefore, the receiver should be placed 80 ft. above the vertex.

The equation of parabola will be:

x² = 4(80)y

x² = 320y