Write a parabola equation with a focus at (-5,1) and a directrix of y=-5

 is the equation of the parabola

Step-by-step explanation:

Let  be any point on the parabola. Find the distance between and the focus. Then find the distance between and directrix. Equate these two distance equations and the simplified equation in and is equation of the parabola.

The distance between and (2,5) is

The distance between and the directrix, y= -5 is

.

Equate the two distance expressions and square on both sides.

Simplify and bring all terms to one side:

=0

Writing the equation with on one side:

This equation in is true for all other values on the parabola and hence we can rewrite with (x,y) .

So, the equation of the parabola with focus (-5, 1) and directrix is y= -5 is

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