What is the equation of the parabola that has a focus of #(0, 8)# and a directrix of #y=-2#?

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Answer 1 · 2017-03-26T10:27:20

#y=1/20x^2+3#

Parabola is a locus of a point which moves so that its distance from a given point called focus and a given line called directrix is always same.

Let the point be #P(x,y)#.

Its distance from #(0,8)# is #sqrt((x-0)^2+(y-8)^2)#

and from #y=-2# is #y+2#

Hence equation is #(x-0)^2+(y-8)^2)=(y+2)^2#

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

or #x^2-20y+60=0# or #y=1/20x^2+3#

graph{x^2-20y+60=0 [-19.42, 20.58, -3.68, 16.32]}