Question

An engineer designs a satellite dish with a parabolic cross-section. The dish is 15 ft. wide at the opening and the depth is 4 feet. Find the position of the light source (the focus). How far is it from the deepest part of the dish?

Answer 1

Answer:

The deepest part of the dish lies at $3.52$ ft

Step-by-step explanation:

The equation of  parabolic  equation is

$X^2 - 4ay = 0$

Where

a signifies the deepest part of the dish or the position of light source from the vortex $V ( 0, 0)$

At $0,0$ co-ordinates the parabola opens up

Solving the above equation, we get

$\frac{15}{2} ^2 = 4 * a * 4$

On solving the above equation for a we get-

$7.5^2 = 4 * 4 * a\\a = \frac{7.5^2}{16} \\a = 3.515$

The deepest part of the dish lies at $3.52$ ft