Respuesta :

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)

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