Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1.

The equation of parabola is .

Explanation:

It is given that the focus of the parabola is (−5, 5) and a directrix of y = −1.

The standard form of a parabola is,

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

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

On comparing both sides we get,

     .... (1)

The directrix of y = −1.

      .... (2)

Add equation (1) and (2),

Put this in equation (1),

Put p=3, k=2 and h=-5 in standard equation of parabola.

Therefore, the equation of parabola is .

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