Question

Franco 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+6y-3x+3=0 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?

Answer 1

Answer: the answer is b (-1.25,-3)

Explanation:

Answer 2

We have to find the focus of the parabola with equation:


`y^(2)+6y-3x+3=0`

In order to find the focus, we first need to convert the equation of parabola to its standard form, as shown below:


`y^(2) + 6y = 3x-3 \\ \\ y^(2) + 2(y)(3) = 3x-3 \\ \\ y^(2) + 2(y)(3) + (3)^(2) = 3x-3 + (3)^(2) \\ \\ (y + 3)^(2) = 3x + 6 \\ \\ (y+3)^(2) = 3(x+2) \\ \\ (y+3)^(2) = 4 * (3)/(4) (x+2)`

Comparing this equation to the similar general equation of parabola, we get:


`(y-k)^(2) = 4p(x-h)`

k = -3
p= 3/4
h = - 2

The focus of the general parabola is located at ( h+p, k)

Using the values, we get:

Focus of the given parabolic satellite =
`(-2+ (3)/(4),-3)=(- (5)/(4),-3)`