Question

Derive the equation of the parabola with a focus at (6,2) and a directix of y=1

Answer 1

The equation of a parabola with focus in (h,k+p) and directrix y=k-p, is,
(x−h)2=4p(y−k)
In the first case,
h=−5k+p=−5y=k−p=7
Combining the last two relations, k=1,p=-6. So the equation of the parabola is,
(x+5)2=−24(y−1)