Find the equation of the parabola with focus (8,0) and vertex (8,6)?

Question

Please help!

Answer 1

This parabola opens downward and has the equation:

4p(y-k) = (x-h)²
where (h,k) is the vertex and p is the distance from vertex to focus. When parabolas open down or to the left, the sign of 4p is negative.

-4(8)(y-6) = (x-8)²
-32(y-6) = (x-8)²

Answer 2

Since only the y coordinate changed between the focus and vertex the parabola opens vertically. The directed distance from the vertex to the focus is p.

p = 0 - 6 = -6
4p = -24

Since p is negative the parabola opens downward.

The equation of a parabola with vertex (h,k) is:

4p(y - k) = (x - h)²

Plug in the values. The equation of the parabola is:

-24(y - 6) = (x - 8)²