Solve Applied Problems Involving Parabolas
-A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 32 feet. If the distance across the top of the mirror is 78 inches, how deep is the mirror in the center?
A) $\frac { 507 } { 512 } \mathrm { in }$.
B) $\frac { 1521 } { 128 } \mathrm { in }$.
C) $\frac { 169 } { 2048 }$ in.
D) $\frac { 256 } { 39 } \mathrm { in }$.

Question

Quizplus · Accepted Answer

The depth of the mirror can be found using the formula for a parabola in vertex form, $y = \frac{1}{4f}x^2$, where $f$ is the focal length. Given the focal length is 32 feet (or 384 inches, since 1 foot = 12 inches) and the distance across the top of the mirror is 78 inches, we substitute $f = 384$ and $x = \frac{78}{2} = 39$ inches (since the distance from the vertex to the edge is half the total width) into the formula to find the depth $y$. This gives $y = \frac{1}{4 \times 384}(39)^2 = \frac{1521}{1536} = \frac{507}{512}$ inches.

Solve Applied Problems Involving Parabolas -A Reflecting Telescope Has a Parabolic

Solve Applied Problems Involving Parabolas
-A Reflecting Telescope Has a Parabolic