What is an equation for the parabola with focus (0, -12) and directrix y = 12

Given:

Focus of a parabola is (0, -12) and directrix is y = 12.

To find:

The equation of the parabola.

Solution:

General form of a parabola is

      ...(i)

where, (h,k) is vertex, (h,k+p) is focus and y=k-p is directrix.

Focus is (0, -12).

        ...(ii)

Directrix is y = 12.

     ...(iii)

Adding (ii) and (iii), we get

Putting k=0 in (ii), we get

Putting h=0, k=0 and p=-12 in (i).

Therefore, the required equation of parabola is .

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step-by-step explanation: