Question

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?

Answer 1

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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