Question

What is the equation of the quadratic graph with a focus of (6, 0) and a directrix of y = −10 ?

Answer 1

The vertex will be exactly half way between the focus and the directrix and in this parabola the vertex will have the same x-coordinate as the focus.
First find the vertex.

Answer 2

ok my teacher knda helped me out and i think i got it. 1/20(x-6)^2+5

Answer 3

I think there may be an easier method. Any point on the parabola is equidistant from the focus and the directrix. Therefore, (x-6)^2 + (y-0)^2 = (y+10)^2
(x-6)^2 + (y-0)^2 = (y+10)^2
(x-6)^2 = (y+10)^2 - y^2
= (y + 10 + y)(y + 10 - y)
= (2y+10)(10)
= 20(y+5)
y+5 = 1/20 * (x-6)^2
y = 1/20 * (x-6)^2 - 5

Answer 4

It is minus 5, not plus 5.

Answer 5

oh man i almost got it. anyways thanks for the steps! i think i can do it now thank you (:

Answer 6

You are welcome.