A searchlight is shaped like a parabola. If the light source is located 3 feet from the base along the axis of symmetry and the

Question

Andrej [43]

4 years ago

10

A searchlight is shaped like a parabola. If the light source is located 3 feet from the base along the axis of symmetry and the

depth of the searchlight is 4 feet, what should the width of the opening of the searchlight be?

Mathematics

1 answer:

Elis [28] · Answer 1 · 2022-03-05T01:41:10+03:00

9514 1404 393

Answer:

8√3 ≈ 13.86 ft

Step-by-step explanation:

The light source is usually placed at the focus, so the focus-vertex distance is p=3 ft. The equation for the parabola with its vertex at the origin is ...

y = 1/(4p)x^2

y = 1/12x^2

The opening for some y-value extends ±x from the axis of symmetry, so is a total of 2x in width.

For y=4, the corresponding value of x is ...

4 = 1/12x^2

48 = x^2

√48 = x = 4√3

Then the width of the searchlight opening is ...

2(4√3 ft) = 8√3 ft ≈ 13.86 ft