Question

A reflecting telescope is purchased by a library for a new astronomy program. The telescope has a horizontal parabolic frame and contains two mirrors, 3 inches apart from each other- the first in the base and the second at the focal point. The astronomy teacher would like to attach a digital monitoring system on the edge of the telescope, creating a straight line distance above the focal point. Assuming that the telescope is placed on the edge of the roof in such a way that it is parallel to the ground, the position of the monitoring system, in relationship to the distance between the base and the focal point is modeled by the equation, x = 1/12y2 (x = the distance between the base and the focal point; y= the height of the monitoring system).
Rewrite the model so that the height of the digital monitoring system is a function of the distance between the base and the focal point of the telescope. How high above the focal point is the digital monitoring system attached to the telescope? Include your function and the height, rounded to the nearest tenth of an inch, in your final answer.

Answer 1

So hmm check the picture below, it looks more or less like so, a parabolic frame with the focus point and on the tip from the stem coming from its center, the digital monitoring system.

$\bf x=\cfrac{1}{12}y^2\implies 12x=y^2\implies \sqrt{12x}=y \\\\\\ \textit{now, what's \underline{y} when x = 3?}\qquad \sqrt{12(3)}=y$