Question

Solar Heat - A mirror is shaped like a paraboloid of

revolution and is used to concentrate the rays of the sun at

its focus, creating a heat source. See the figure. If the mirror

is 20 feet across at its opening and is 6 feet deep, where will

the heat source be concentrated?

Short answer

The heat source will be concentrated at 4.17 ft .

Step-by-step solution

Step 1.  Given information .

Consider the given distance and depth .

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 focus is on the y positive axis .

Step 3. Find the distance .

To find the distance of heat source substitute the values $x=\frac{20}{2}=10,y=6$in the standard form of parabola .

$$\begin{gathered} x^2=4ay \\ {\left(10\right)}^2=4a·6 \\ a=4·17ft \end{gathered}$$

Therefore the heat source will be concentrated at$4·17ft$