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# Which equation represents a parabola that has a focus of (0, 0) and a directrix of y = 2?

x^{2} = -(y - 1)

x^{2} = -4y

x^{2} = -y

x^{2} = -4(y - 1)

**Solution:**

Given: Focus of parabola (0, 0) and a directrix of y = 2

Vertex is midway between focus and directrix.

Therefore vertex is at (0, 1)

The vertex form of equation of parabola is y = a(x - h)^{2 }+ k

Where vertex h = 0 and k = 1

So the equation of parabola is y = a(x - 0)^{2 }+ 1

Distance of vertex from directrix is d = 2 - 1 = 1,

We know d = y = k - 1/4a

2 = 1 -1/4a

1/4a = -1

a = -1/4

Here the directrix is above the vertex, so the parabola opens downward and a is negative.

Therefore, the equation of parabola is y = -1/4x^{2 }+ 1

## Which equation represents a parabola that has a focus of (0, 0) and a directrix of y = 2?

**Summary:**

This x^{2} = -4(y - 1) equation represents a parabola that has a focus of (0, 0) and a directrix of y = 2.

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