Question

Mustafa is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. The shape of his satellite can be modeled by (y+2)^2=9(x-2) where x and y are modeled in inches. He 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?

(4.25, –2)
(4.25, 0)
(4.25, 2)
(4.25, 4)

Answer 1

(4.25, -2) is the focus point

Answer 2

A. (4.25, –2)

Explanation:

We are given that,

The shape of the satellite is modeled by the function,
`(y+2)^2=9(x-2).`

Since, the equation of a parabola is
`(y-k)^2=4p(x-h)` .

So, on comparing, we have,

h= 2, k= -2 and
`4p=9`

i.e. h= 2, k= -2 and
`p=(9)/(4)`

As, the focus point is (h+p,k).

So, we get,

The focus point =
`(2+(9)/(4),-2)`

i.e. The focus point =
`((17)/(4),-2)`

i.e. The focus point = (4.25,-2)

Hence, the focus point of the satellite is (4.25,-2).