Solve the problem.
-A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex to the focus is 31 feet and the distance across the top of the mirror is 66 inches, how deep is the mirror in the center?
A) $\frac { 121 } { 1984 }$ in.
B) $\frac { 363 } { 496 }$ in.
C) $\frac { 961 } { 132 }$ in.
D) $\frac { 1089 } { 124 } \mathrm { in } .$

Question

Quizplus · Accepted Answer

The depth of the mirror can be found using the formula for a paraboloid of revolution, $y = \frac{1}{4f}(x^2)$, where $f$ is the focal length and $x$ is the distance from the vertex. Given the focal length is 31 feet (or 372 inches, converting feet to inches) and the diameter of the mirror is 66 inches (thus the radius, $x$, is 33 inches), we substitute these values into the formula to find the depth, $y$. This gives $y = \frac{1}{4 \times 372}(33)^2 = \frac{1089}{1488} = \frac{363}{496}$ inches.

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