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

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:

$y^{2} + 6y = 3x-3 \\ \\ y^{2} + 2(y)(3) = 3x-3 \\ \\ y^{2} + 2(y)(3) + (3)^{2} = 3x-3 + (3)^{2} \\ \\ (y + 3)^{2} = 3x + 6 \\ \\ (y+3)^{2} = 3(x+2) \\ \\ (y+3)^{2} = 4 * \frac{3}{4} (x+2)$

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 = $(-2+ \frac{3}{4},-3)=(- \frac{5}{4},-3)$

Answer 2

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

Step-by-step explanation: