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 depth of the searchlight

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

Short answer

The width of the opening is$4\sqrt{2}$.

Step-by-step solution

Step 1. Given information .

Consider the given distance from the base and depth .

Step 2. Standard form of parabola used.

The standard form of parabola is $x^2=4ay$.

Step 3. Find the width .

To find the width of searchlight substitute $a=2,y=4$in the standard form of parabola .

$$\begin{gathered} x^2=4ay \\ {x}^2=4·2·4 \\ {x}^2=32 \\ x=\sqrt{32}=4\sqrt{2} \end{gathered}$$

Therefore the width of the searchlight is$4\sqrt{2}$.