Question

Searchlight - 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 5 feet across,

how deep should the searchlight be?

Short answer

The depth of the searchlight is 0.781 ft.

Step-by-step solution

Step 1. Given information .

Consider the given distance from the base and opening .

Step 2. Standard form of parabola used .

The standard form of parabola is $x^2=4ay$the vertex of the parabola is at origin and the focus is on y positive axis .

Step 3. Find the depth .

To find the depth of the searchlight substitute $x=2·5a=2$in the standard form of parabola .

$$\begin{gathered} x^2=4ay \\ {\left(2·5\right)}^2=4·2y \\ y=0·781ft \end{gathered}$$

Therefore the depth of the searchlight will be $0·781ft$.