Answer:
The searchlight should be 6.25ft deep
Step-by-step explanation:
Given
[tex]Across = 20ft[/tex]
[tex]Base = 4ft[/tex]
Required
The depth of the searchlight
[tex]Across = 20ft[/tex] implies that the search light span 10 units to either side of the x-axis
[tex]Base = 4ft[/tex] 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:
[tex](x,y) = \{(-10,4), (10,4)\}[/tex]
The depth (a) of the search light is calculated using:
[tex]x^2 = 4ay[/tex]
Make a the subject
[tex]a = \frac{x^2}{4y}[/tex]
Substitute -10 or 10 for x and 4 for y
[tex]a = \frac{(-10)^2}{4*4}[/tex]
[tex]a = \frac{100}{16}[/tex]
[tex]a = 6.25ft[/tex]
