A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the opening is 12 feet across, how deep should the searchlight be?

3 ft.

Step-by-step explanation:

We have that the parabola formula has the following general equation:

x ^ 2 = 4py

p would come being the distension of the vertex until the focus.

They tell us that this value is 3, that is to say p = 3. Replacing we have:

x ^ 2 = 4 * 3 * y

x ^ 2 = 12 * y

reorganizing for and, we are left with:

y = (1/12) * x ^ 2

We know that the opening is 12 feet wide, therefore, the parabola, being symmetry, must be distributed in the same way, in two equal parts, that is, 12/2 = 6. Therefore, being vertical on the x axis must take values of (-6, y), (6, y).

Which means that the value of x is 6 or -6. (it doesn't matter which of the two is when it is squared)

Replacing in the equation obtained:

y = (1/12) * (6 ^ 2)

y = 3

Therefore the depth is equal to 3 ft.