How do you find the equation of a parabola with vertex at the origin and directrix x=3?

1 Answer
Feb 24, 2017

Answer:

#y^2+12x=0#

Explanation:

As we have vertex at the origin i.e. #(0,0)# and directrix is #x=3#, a line parallel to #y#-axis,

it must have a focus at #(-3,0)#.

Equation of the parabola represents locus of a point #(x,y)#, which moves so that its distance from #x=3# and #(-3,0)# are equal. Hence, equation of parabola is

#(x-(-3))^2+(y-0)^2=(x-3)^2#

or #(x+3)^2+y^2=(x-3)^2#

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

or #y^2+12x=0#
graph{y^2+12x=0 [-27.59, 12.41, -10.08, 9.92]}