Question

The focus of a parabola is (-10, -7), and its directrix is x = 16. Fill in the missing terms and signs in the parabola's equation in standard form.

Answer 1

Answer: (y + 7)^2 = - 52(x - 3)

Explanation:

Answer 2

Answer: (y-3)^2= 52(x+7)

The focus is (-10, -7) and the directrix is x=16. The y-coordinate of the vertex should be same as the focus(k=-7). Then the x-coordinate of the vertex would be:
p + (-10)= 16 - p
2p= 16 + 10
p=26/2= 13

The x-coordinate of the vertex would be:
h= p+ (-10)
h= 13 - 10= 3

The vertex coordinate would be: (h, k)= (3, -7)
For a vertex (h, k), the formula for equation would be
(y-k)^2=4 p(x-h)
(y-3)^2= 4*13(x--7)
(y-3)^2= 52(x+7)