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

Answer 2

The position of the light source(the focus) is at; (0, 3.516).

The distance from the position of light source to the deepest part of dish is; 3.516 ft.

We know that standard form of a parabola equation is;

x² = 4ay

Now, we are told the dish is 15 ft wide and the depth is 4ft.

This means that the edge of the parabolic cross section will have an x-coordinate of 15/2 = 7.5 ft

While the y-coordinate is the depth of 4ft.

Thus;

Since;

x² = 4ay

Plugging in 7.5 ft for x and 4 ft for y gives;

7.5² = 4a(4)

a = 7.5²/16

a = 3.516 ft

Thus, position of the light source which is the focus is; (0, 3.516)

And distance from the position of light source to the deepest part of dish = 3.516 ft.

Read more at; https://brainly.com/question/3513488