Which equation represents a parabola that has a focus of (0 0) and a directrix of y = 2 1. x^2 = - (y-1) 2. x^2 = -4y 3. x^2 = -y 4. x^2 = -4 (y-1)

4.

Step-by-step explanation:

Given,

Focus of parabola = (0,0)

And, directrix is, y = 2,

Thus, the parabola must be along y-axis,

We know that,

The standard form of a parabola along y-axis,

Where, focus = (h, k+p)

And, directrix, y = k-p

Thus, we can write,

h = 0, k+p = 0

k-p = 2

⇒ k+p + k-p = 0 + 2

⇒ 2k = 2 ⇒ k = 1

⇒ 1 - p = 2 ⇒ p = - 1

Hence, the equation of the parabola is,

Option 4 is correct.

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