A parabola can be drawn given a focus of (0, 2) and a directrix of y = 0. Write the equation of the parabola in any form.

Given:

Focus of a parabola = (0,2)

Directrix: y=0.

To find:

The equation of parabola.

Solution:

The equation of parabola is

      ...(i)

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

Focus :

On comparing both sides, we get

         ...(ii)

On comparing y=k-p and y=0, we get

         ...(iii)

Adding (ii) and (iii), we get

Putting k=1 in (ii).

Putting h=0, k=1 and p=1 in (i).

Therefore, the equation of required parabola is .

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