Determine the equation of the parabola with focus (-6,-7) and directrix y=9

Answer 1

Use the slider for x1 on the following graph to show that distances from any point on the parabola to the focus and to the directrix are equal.

desmos.com/calculator/k3uxcu8gpm

Answer 2

Answer 3

Given a focus F = (f₁, f₂), and directrix ax+by+c=0, we have the parabola given by

(ax+by+c)² = (a²+b²)((x-f₁)²+(y-f₂)²). So your problem has a = 0, b=1, c=-9, F=(-6,-7) thus we have

(y-9)²=(x+6)²+(y+7)²