Answer: (y - 9)^2 = -48(x - 7)
Explanation:
To find the equation of the parabola in standard form, we can use the formula (y - k)^2 = 4p(x - h), where (h, k) is the vertex and p is the distance between the vertex and the focus.
Given that the vertex is (7, 9) and the focus is (-5, 9), we can see that the vertex and focus have the same y-coordinate, which means the parabola opens horizontally.
The vertex is (h, k) = (7, 9) and the focus is (h + p, k) = (-5, 9). By comparing the x-coordinates, we can find p.
-5 = 7 + p
p = -12
Substituting the values into the formula, we get:
(y - 9)^2 = 4(-12)(x - 7)
So, the equation of the parabola in standard form is (y - 9)^2 = -48(x - 7).
(hope this helped)