Question

50 POINTS PLEASE SHOW WORK!!!! 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

In this exercise we have to use the knowledge of depth to be able to calculate the depth that is being seen by the telescope, in this way we can say that:

45 feet deep

First, knowing that the formula for the parabola is:

4py=x²

Now P is the distance from the vertex to the focus or to the directrix which is equal to 20, we can say that:

4(20)y=x²

80y=x²

Now we just should use individual knwon financial worth of X fashionable the maximum point of the dish, exist the measurement across object of the eating receptacle exist 120 extremities that is to say the maximum x, and we understand information that 120 extremities is heavy distance middle from two points the expansive -x and x, so those hopeful: -60 and 60.

80y=x²

80y=60²

80y=3600

y=45

Answer 2

75ft

Explanation:

We can let the parabola open upward......so we will have the form

4a ( y - k) = (x - h)^2

The distance from the vertex to the focus = 20 = a

We can let the vertex be ( 80, 30)

So we have the form

4(20) ( y- 30) = (x - 80)^2 simplify

80 ( y - 30) = ( x - 80)^2

Since the diameter is 120 ft...the radius is 60 ft.....so we can let one point on the parabola be ( 80 + 60 , a) =

(140 , a)......where a is the height of the dish....so we have that

80 ( a - 30) = (140 - 80)^2

80 ( a - 30) = (60)^2

80 ( a - 30) = 3600 divide both sides by 80

a - 30 = 45 add 30 to both sides

a = 75 ft = the height of the dish