What is the equation of the parabola with a focus at (-3,-7) and a directrix of y= 2?

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Answer 1 · 2017-01-24T11:13:26

The equation is #(x+3)^2=-18(y+5/2)#

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

Therefore,

#(y-2)=sqrt((x+3)^2+(y+7)^2)#

#(y-2)^2=(x+3)^2+(y+7)^2#

#cancely^2-4y+4=(x+3)^2+cancely^2+14y+49#

#-18y-45=(x+3)^2#

#-18(y+45/18)=(x+3)^2#

#-18(y+5/2)=(x+3)^2#

The vertex is #V=(-3,-5/2)#

graph{((x+3)^2+18(y+5/2))(y-2)((x+3)^2+(y+5/2)^2-0.02)=0 [-25.67, 25.65, -12.83, 12.84]}