True of False? The equation of a parabola with its vertex at the origin and its directrix y = 7/4, is the equation x^2= -7y.

Answer 1

The given equation is in the form of x²=4ay where the directrix is y=-a.

If we assume the directrix is y=7/4, then a=-7/4, so the equation should be x²=4(-7/4)y --> x²=-7y

Since the above equation matches the given equation in the problem, the answer is true.

Hope this helped!

Answer 2

directrix y = 7/4, vertex at the origin (0,0)

parabola is x^2 = -7y is a downward opening vertical parabola

with a horizontal directrix, usually written in vertex form as y = (-1/7)x^2

negative sign means it's downward opening

focus is (0, -7/4) equidistant with the directrix from the vertex, just in the opposite direction

answer to the problem is true