How do you find the equation of the parabola with the given focus F(-2,0) and directrix x=8?

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Answer 1 · 2017-08-09T14:32:56

The equation of the parabola is #y^2=-20(x-3)#

Any point #(x,y)# on the parabola is equidistant from the focus #F=(-2,0)# and the directrix #x=8#

Therefore,

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

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

#x^2+4x+4+y^2=x^2-16x+64#

#y^2=-20x+60=-20(x-3)#

graph{y^2=-20(x-3) [-3.82, 7.28, -2.44, 3.107]}