Question

A searchlight is shaped like a paraboloid of revolution. If the light source is located 4 feet from the base along the axis of symmetry and the opening is 20 feet​ across, how deep should the searchlight​ be?

Answer 1

The searchlight should be 6.25ft deep

Explanation:

Given

`Across = 20ft`

`Base = 4ft`

Required

The depth of the searchlight

`Across = 20ft` implies that the search light span 10 units to either side of the x-axis

`Base = 4ft` implies that the search light span 4 units to the y-axis

The attached image illustrates the revolution.

From the attached image, the endpoints of the searchlight is:

`(x,y) = \{(-10,4), (10,4)\}`

The depth (a) of the search light is calculated using:

`x^2 = 4ay`

Make a the subject

`a = (x^2)/(4y)`

Substitute -10 or 10 for x and 4 for y

`a = ((-10)^2)/(4*4)`

`a = (100)/(16)`

`a = 6.25ft`