Question

Which is the equation of a parabola with Vertex (0,0) and directrix y=4?

a p = -8x

c. x² = -87

b. ² = -16x

d x2 =-16y

Please select the best answer from the choices provided

Answer 1

x² = -16y

Explanation:

We are given:

Vertex (0,0)

Directix y = 4

Here we are asked to find the equation of a parabola given the above conditions.

The standard form of a parabola is

x² = 4ay................ (1)

directix y = -a...........(2)

In this question, we are given directix y = 4, so lets substitute 4 for y in the equation 2 above.

Thus, we have:

4 = -a

a = -4

Let's now substitute -4 for -a in equation 1.

x² = 4ay

x² = 4 * -4 * y

x² = -16y

Therefore, the equation of a parabola with Vertex (0,0) and directrix y=4 is (x² = -16y)