Question

Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2.

y2 = 2x
y = one divided by twox2
y2 = 8x
y = one divided by eightx2

Answer 1

ok... so the distance from the directrix to the focus is needed.



so by plotting the information the vertex is halfway between the focus and directrix
on the line x = 0.

the distance from the focus to the vertex is called the focal length, a

so use the standard form of the equation

\[(x - h)^2 = 4a(y - k)\]

(h, k) is the focus.... and a is the focal length.

You know h = 0, just find k.... remember halfway between the focus and directrix

and a is the distance from the vertex to the focus...

hope it helps

Answer 2

when you get it into the standard form, make y the subject.