Find the equation of parabola, whose directrix is #y=9# and vertex is #(0,0)#?

1 Answer
Nov 26, 2017

#y=-1/36x^2#

Explanation:

We have directrix as #y=9# and vertex is #(0,0)#. As vertex is in between focus and directrix

focus is #(0,-9)# and equation of parabola is locus of a point #(x,y)#, which moves so that its distance from directrix #y=9# and focus #(0,-9)# is always equal and hence

#sqrt((x-0)^2+(y+9)^2)=|y-9|#

or squaring each side #x^2+y^2+18y+81=y^2-18y+81#

or #36y=-x^2# or #y=-1/36x^2#

graph{(36y+x^2)(y^2+x^2-0.4)((y+9)^2+x^2-0.4)(y-9)=0 [-40, 40, -20, 20]}