A parabola can be drawn given a focus of ( 7 , − 4 ) (7,−4) and a directrix of y = − 10 y=−10. Write the equation of the parabola in any form.

Answer 1

The easiest form to use is (x-h)^2 = 4p(y - k), where

the vertex is at (h, k),the directrix is p below the vertex, and the focus is p above.

As the focus is (7, -4) and the directrix is y =-10, k = (-4 - 10)/2 = -7, and h, read from the x coordinate of the focus, is 7

From the location of the focus and vertex, p = -4 - -7 = 3

Thus, our parabola is (x - 7)^2 = 4*3*(y - -7) or

(x-7)^2 = 12(y+ 7)

Answer 2

The vertex will be equidistant from the focus to the directrix so the vertex is at (7,-7) and the focal length (p) =3

The equation would be be 4p(y-k) = (x-h)^2

12(y+7) =(x-7)^2

(y+7) = 1/12(x-7)^2

y=1/12(x-7)^ -7