A parabola can be drawn given a focus of (5,6) and a directrix of y = 2. Write the equation of the parabola in any form.

Given:

Focus of the parabola = (5,6)

Directrix of the parabola is y=2.

To find:

The equation of the parabola.

Solution:

The equation of the parabola is:

            ...(i)

Where, (h,k) is vertex, (h,k+p) is focus and is the directrix.

It is given that the focus of the parabola is at (5,6).

On comparing both sides, we get

           ...(ii)

Directrix of the parabola is y=2. So,

            ...(iii)

Adding (ii) and (iii), we get

Putting in (ii), we get

Putting in (i), we get

Therefore, the equation of the parabola is .

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