A satellite dish is being designed so that it can pick up radio waves coming from space. The satellite dish will be in the shape of a parabola and will be positioned above the ground such that its focus is 50 ft above the ground. Using the ground as the x-axis, where should the base of the satellite be positioned? Which equation best describes the equation of the satellite?

(0, 25); y = one over one hundredx2 − 25

(0, 50); y = one over two hundredx2 − 50

(0, 25); y = one over one hundredx2 + 25

(0, 50); y = one over two hundredx2 + 50

Let the ground be at (0,0). The base should be located at the midpoint between the ground and the focus (0,50). The position of the base of the satellite is:

[tex]B=(\frac{0+0}{2},\frac{0+50}{2} )\\B=(0,25)[/tex]

The base (vertex) is at (0, 25).

A parabola can be described by the following general formula:

[tex]4a(y-k)=(x-h)^2[/tex]

Where h = 0, k = 25 and a =50 -25 =25.

The equation for the parabola is:

[tex]4*25(y-25)=(x)^2\\100y=x^2+2,500\\y=\frac{x^2}{100}+25[/tex]

Therefore, the answer is:

(0, 25); y = one over one hundredx2 + 25

JackelineCasarez JackelineCasarez · Answer 2 · 2022-01-15T18:53:07+01:00

The equation that most adequately recounts the satellite's equation would be:

C). (0, 25); y = one over one hundredx^2 + 25

Assuming the ground level being at [tex](0, 0)[/tex].

So, the base would lie between [tex](0, 50)[/tex] i.e. between ground and the point of focus.

This will lead the base's position to lie at;

[tex]B = [(0 + 0)/2, (0 + 50)/2][/tex]

∵ [tex]B = (0, 25)[/tex]

Using the parabola,

[tex]4a(y - k) = (x - h)^2[/tex]

Now by putting the values,

[tex]4(50) (y - 25) = (x - 0)^2[/tex]

⇒ [tex]100y = x^2 + 2,500[/tex]

⇒ [tex]y = (x^2/100) + 25[/tex]

∵ (0, 25) y = one over one hundredx^2 + 25 i.e option C is the correct answer.

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