What is the vertex form of the equation of the parabola with a focus at (2,-8) and a directrix of #y=-3#?

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Answer 1 · 2018-06-29T07:24:30

The vertex form is #y=-1/10(x-2)^2-55/10#

Any point #(x,y)# on the parabola is equidistant from the directrix and the focus.

#y+3=sqrt((x-2)^2+(y+8)^2)#

Squaring both sides

#(y+3)^2=(x-2)^2+(y+8)^2#

Expanding

#y^2+6y+9=(x-2)^2+y^2+16y+64#

#10y=-(x-2)^2-55#

#y=-1/10(x-2)^2-55/10#

graph{-1/10(x-2)^2-55/10 [-23.28, 28.03, -22.08, 3.59]}