What is the standard form of the equation of the parabola with a directrix at x=-3 and a focus at (5,3)?

1 Answer
Jan 3, 2016

The Equation of the Parabola is # x = 16*y^2 -96*y +145 #

Explanation:

graph{x=16y^2-96y+145 [-10, 10, -5, 5]}

Here the focus is at (5,3) and directrix is x = -3 ; We know the Vertex

is at equidistance from focus and directrix. So the vertex co-

ordinate is at (1,3) and the distance p between vertex and directrix is

#3+1=4#. We know the equation of parabola with vertex at (1,3)

and directrix at x=-3 is #(x-1) = 4 *p *(y-3)^2# or #x-1 = 4*4*(y-3)^2#

or #x-1 = 16y^2- 96y+ 144# or #x = 16*y^2 -96*y +145#[answer]