Question

HELP PLEASE !! FAN AND MEDAL
find the equation for the parabola given focus(-2,-4) and directrix x= 6

Answer 1

essentially, you could just use the definition of a parabola to define all points (x,y) that are the same distance from the focus and the directrix

Answer 2

do you know the distance formula?

Answer 3

the point that you are an equal distance from the directrix, has a constant x=6, and y=y giving us the relationship
\[(x--2)^2+(y--4)^2=(x-6)^2+(y-y)^2\]

the rest is just simplifications