Question

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

Answer 1

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]