Answer
$569.63in$.
Work Step by Step
Step 1. Set up a general equation for the parabola: let the vertex of the mirror be at the origin and its focus on the +y-axis, the general equation can be written as $x^2=4py$ with its focus at $(0,p)$.
Step 2. Identify the given conditions: the coordinates of one end of the mirror is given as $(100, 3.79)$ as shown in the figure of the Exercise.
Step 3. Plug the coordinates in the general equation: $100^2=4p×3.79$ and we get $p\approx569.63in$.
Step 4. Conclusion: the focal length of the mirror is $569.63in$.
