Question

Derive the equation of the parabola with a focus at (-5, 5) and a directrix of y = -1. (2 points) Please help

Answer 1

We see that the the parabola opens up since directix is below the focus

for an parabolla opening up/down with vetex at (h,k) and the distance from teh vertex to the focus is p
$(x-h)^2=4p(y-k)$
the distance from vertex to directex is the same as from focus to directix

from (-5,5) and y=-1
that is  a vertical distance of 6
vertex is in the middle
6/2=3
5-3=2
the vertex is at (-5,2)
the distance is 3
$(x-(-5))^2=4(3)(y-(2))$
$(x+5)^2=12(y-2)$
$y=\frac{1}{12}(x+5)^2+2$