Write the equation for a parabola with a focus at (−4,8)(-4,8)(−4,8)left parenthesis, minus, 4, comma, 8, right parenthesis and a directrix at x=−6x=-6x=−6x, equals, minus, 6.

Given:

The focus of the parabola is at (-4,8).

The directrix is at x=-6.

To find:

The equation of the parabola.

Solution:

The directrix is at x=-6, which is a vertical line. So, the parabola is horizontal.

The equation of a horizontal parabola is

Where, (h,k) is vertex, (h+p,k) is focus and x=h-p.

The focus of the parabola is at (-4,8).

            ...(i)

The directrix is at x=-6.

           ...(ii)

Adding (i) and (ii), we get

Putting h=-5 in (i), we get

Putting h=-5, k=8 and p=1 in the standard form of the parabola.

Therefore, the required equation of the parabola is .

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step-by-step explanation: