What is the equation of the parabola with a focus at (0,0) and a directrix of y= 3?

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Answer 1 · 2018-06-28T08:50:52

#x^2=-6y+9#

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

Let the point be #(x,y)# and its distance from #(0,0)# is #sqrt(x^2+y^2)#

and its distance from directrix #y=3# is #|y-3|#

and hence equation of parabola is

#sqrt(x^2+y^2)=|y-3|# and squaring

#x^2+y^2=y^2-6y+9#

or #x^2=-6y+9#

graph{(x^2+6y-9)(y-3)(x^2+y^2-0.03)=0 [-10, 10, -5, 5]}