What is the equation of the parabola with a focus at (-5,23) and a directrix of y= 14?

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Answer 1 · 2017-08-05T08:29:41

The equation of the parabola is #(x+5)^2=3(6y-111)#

Any point #(x,y)# on the parabola is equidistant from the focus #F=(-5,23)# and the directrix #y=14#

Therefore,

#sqrt((x+5)^2+(y-23)^2)=y-14#

#(x+5)^2+(y-23)^2=(y-14)^2#

#(x+5)^2+y^2-46y+529=y^2-28y+196#

#(x+5)^2=18y-333#

graph{((x+5)^2-18y+333)(y-14)=0 [-70.6, 61.05, -18.83, 47]}