Question

Please Help!!

Find the standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8.

Answer 1

The Vertex is exactly between the two given items. Find that, first.

Answer 2

hmmm....

Answer 3

u mean write the equation or no @ninjasandtigers

Answer 4

y = 1/32x^2

y^2 = 8x

y^2 = 32x

y = 1/8x^2

Answer 5

between 0 and 8? @tkhunny

Answer 6

Well, the problem choices gave it away. Clearly (0,0). Lame.

Answer 7

Directrix is y = Something, so this must be vertically oriented. Throw out the ones with y^2.

Answer 8

|Directrix to Vertex| = 8 = The Mysterious "p".
|Vertex to Focus| = 8 = The Mysterious "p".

That's enough information. You can just build it, now.

Answer 9

thank you

Answer 10

so is it d?

Answer 11

Another way to do this problem is to make use of the property of the parabola that any point on the parabola is equidistant from the focus and the directrix:

(x-0)^2 + (y-8)^2 = (y - (-8))^2
x^2 = (y+8)^2 - (y-8)^2
x^2 = (y+8+y-8)(y+8-y+8)
x^2 = 2y*16
y = 1/32x^2

Answer 12

Always, Always, think about using the definition. It may be more difficult than some specific method, but it ALWAYS works.