Question

Samara 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 y^2=2(x+6), 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

Answer:

(-5.5,0)

Step-by-step explanation:

The question is on finding the focus point of a parabola

Given y²= 2(x+6).....................................(a)

Compare equation (a) with the standard equation  (y-b)²= 2p(x-a)

y²= 2(x+6)------can be written as (y-0)²=2(x+6)

(y-0)²=2(x+6)

(y-b)²= 2p(x-a)

2p=2-----------------divide both sides by 2 to get p

p=2/2=1

For  the vertex (a,b)⇒(-6,0)

For  the focus point ( a+p/2, b)........................................(b)

Substitute values i equation (b) above

(-6+1/2 ,0) =(-5.5, 0)