Question

A radio telescope has a parabolic dish. Radio signals are collected at the focal point (focus) of the parabola. The distance from the vertex of the parabolic dish to the focus is 20 feet. The vertex of the dish is located at a point 30 feet above the ground and 80 feet to the east of a computer that reads and records data from the telescope. The diameter of the dish is 120 feet.
What is the depth of the parabolic dish?

Answer 1

Answer:

45 feet deep

Step-by-step explanation:

First the formula for Parabola is: 4py=x2, we will make it as if it were in the center of the graph.

Now P is the distance from the vertex to the focus or to the directrix which is equal to 20.

4(20)y=x2

80y=x2

Now we just have to use one knwon value of X in the maximum point of the dish, is the diameter of the dish is 120 feet that is the maximum x, and we know that 120 feet is te distance between the widest -x and x, so those would be: -60 and 60.

We will use 60 as our value:

$80y=x^{2} \\80y=60^{2} \\80y=3600\\y=\frac{3600}{80} \\y=45$

So we know that the depth of the parabolic dish is 45 feet.