What is the equation in standard form of the parabola with a focus at (-10,8) and a directrix of y= 9?

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Answer 1 · 2017-08-05T13:11:45

The equation of the parabola is #(x+10)^2=-2y+17=-2(y-17/2)

Any point #(x,y)# on the parabola is equidistant from the focus #F=(-10,8)# and the directrix #y=9#

Therefore,

#sqrt((x+10)^2+(y-8)^2)=y-9#

#(x+10)^2+(y-8)^2=(y-9)^2#

#(x+10)^2+y^2-16y+64=y^2-18y+81#

#(x+10)^2=-2y+17=-2(y-17/2)#

graph{((x+10)^2+2y-17)(y-9)=0 [-31.08, 20.25, -9.12, 16.54]} #