Write the equation for a parabola with a focus at (-3,-5)(−3,−5) and a directrix at x=-7

1 answer

Recall that the parabola
y^2 = 4px
has its
focus at (p,0)
directrix at x = -p
vertex is midway between the focus and the directrix, at (-5,-5)
So, here we clearly have p = 2
So the equations is
(y+5)^2 = 8(x+5)^2

see
https://www.wolframalpha.com/input/?i=parabola+%28y%2B5%29%5E2+%3D+8%28x%2B5%29
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