Question

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?

Answer 1

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)

Answer 2

Hello,
Please, see the attaced file.
Thanks.