1. ## 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 26 feet and the distance across the top of the mirror is 58 inches, how deep is the mirror in the center?

2. Hello, m3tbaby954!

A reflecting telescope has a mirror shaped like a paraboloid of revolution.
If the distance of the vertex to the focus is 26 feet
and the distance across the top of the mirror is 58 inches,
how deep is the mirror in the center?
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$\text{The equation of the parabola is: }\:x^2 \:=\:4py$
. . $\text{where }p\text{ is the distance from the vertex to the focus.}$

$\text{Since }p = 26\text{, we have: }\:x^2 \:=\:104y$

$\text{When }x = 29\text{, we have: }\;29^2 \:=\:104y \quad\Rightarrow\quad y \:=\:\frac{841}{104}$

The depth of the mirror is about 8.09 feet.