Which equation represents a parabola that has a focus of (0, 0) and a directrix of y = 4?

x^2=−8y

x^2=−8(y−2)

x^2=−2(y−2)

x^2=−2y

jjennylove Feb 6, 2019

#1**+2 **

If the directri is y = 4 and the focus is (0,0).....the vertex = (0, (0 + 4)/2 ) = (0, 2 )= (h, k)

In other words....the vertex is midway between the focus and the directrix

p is the distance between the vertex and the focus = 2

And since the directrix is above the focus, the parabola opens downward

And we have the form

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

-4p(y-2) = x^2 (we use the " - " because the parabola opens downward )

- 4(2) (y -2) = x^2

-8(y - 2) = x^2

EDIT TO CORRECT AN ERROR

CPhill Feb 6, 2019