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Deanna is adjusting a satellite because she finds it is not focusing the incoming radio waves perfectly. The shape of her satellite can be modeled by x^2=12y where x and y are modeled in inches. She realizes that the static is a result of the feed antenna shifting slightly off the focus point. What is the focus point of the satellite?

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Answer:

The shape of satellite which is in the shape of parabola, opening upwards is, \(x^2=12 y\), having vertex (0,0).

Comparing with general equation of parabola

\(x^2=4 a y\) , having vertex (0,0) and focus (0,a).

Comparing the two above equation of parabola

4 a y = 12 y

4 a = 12

a=3

So, focus of the satellite which is in the shape of parabola=(0,3)

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