PLEASE HELP!!!!! A satellite telescope has a parabolic dish. Satellite signals are collected at the focal point (focus) of the
parabola. The distance from the vertex of the parabolic dish to the focus is 40 feet. The vertex of the dish is
located at a point 50 feet above the ground and 100 feet to the east of a computer that reads and records
data from the telescope. The diameter of the dish is 160 feet.

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MrRoyal MrRoyal · Answer 1 · 2021-10-30T13:39:44+02:00

The dish illustrates operations on a parabola.

The depth of the parabolish dish is 160 feet.

The bowl is said to be a parabola.

So, we have:

[tex]\mathbf{(x -h)^2 = 4p(y - k)}[/tex]

Where:

[tex]\mathbf{Focus: p = 40}[/tex]

[tex]\mathbf{Vertex:(h,k) = (0,0)}[/tex]

From the question, the diameter is 160 feet.

So, the radius (r) is:

[tex]\mathbf{r = \frac{160}{2} = 80}[/tex]

So, the coordinate of the depth of the parabola would be:

[tex]\mathbf{(x,y) = (60 + 100,y)}[/tex]

[tex]\mathbf{(x,y) = (160,y)}[/tex]

Substitute these values in [tex]\mathbf{(x -h)^2 = 4p(y - k)}[/tex]

So, we have:

[tex]\mathbf{(160 - 0)^2 = 4 \times 40 \times (y -0)}[/tex]

[tex]\mathbf{160^2 = 160y}[/tex]

Divide both sides by 160

[tex]\mathbf{160 = y}[/tex]

Rewrite as:

[tex]\mathbf{y = 160 }[/tex]

Hence, the depth of the parabolish dish is 160 feet.