Practice!

Sample Problem

Find the standard form of the equation of a parabola with a focus (1, -3) and directrix y=-7.

Solution

Because the axis of the parabola should be the perpendicular to the directrix, we know that the axis of the parabola needs to be vertical (since the directrix is horizontal). Therefore, we’ll use the equation

(x-h)2=4p(y-k)

where h=1 (the vertex has the same x-coordinate as the focus)

On the other hand, we know that p>0 (the directrix is located below the focus),

so the y-coordinate of the focus=k+p=-3 and the directrix has the equation y=k-p=-7

k+p=-3

k-p=-7

2p=4

p=2 and k=-5

(x-h)2=4p(y-k)

Where h=1, k=-5, and p=2

(x-1)2=8(y+5)