Answer:
The equation of the parabola is (x-2)^2 = 48(y-5)
Step-by-step explanation:
Mathematically, we can obtain the equation of a parabola from its focal point and the directrix given.
Firstly, we need to find the distance between the director and the vertex
That would be ;
|-7-(5)| = 12
We should kindly note that the directrix is below the vertex and thus it is a right-side parabola with a positive value of p = 12
Thus, the equation needed would be;
(x-h)^2 = 4p(y-k)
From the question, h = 2
p = 12 ( calculated) and k = 5
So the equation would be;
(x-2)^2 = 4(12)(y-5)
= (x-2)^2 = 48(y-5)
