Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7

Given:

The focus of the parabola is at (6,-4).

Directrix at y=-7.

To find:

The equation of the parabola.

Solution:

The general equation of a parabola is:

                 ...(i)

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

The focus of the parabola is at (6,-4).

On comparing both sides, we get

                           ...(ii)

Directrix at y=-7. 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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