How do you find the equation of a parabola with vertex at the origin and directrix x=-2?

1 Answer
Jan 24, 2017

Answer:

#y^2=8x#

Explanation:

The standard form of the parabola is #y^2=4ax#, giving a parabola with its axis parallel to the #x#-axis, vertex at the origin, focus #(a,0)# and directrix #x=-a#. So in your case #a=2#, giving #y^2=4ax#.

Alternatively, you can work from a definition of a parabola, which is the set of all points #(x,y)# such that the distance from the point to the directrix #x=-2# is the same as the distance to the focus (2,0)#.
(The vertex is half-way between the focus and the directrix.)

#(x-(-2))^2=(x-a)^2+y^2#
#cancel(x^2)+4ax+cancel 4=cancel(x^2)-4ax+cancel 4+y^2#
#y^2=4ax+4ax=8ax#