SOLUTION: Find the equation of the parabola with focus at (8,0) and directrix x=-8

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the equation of the parabola with focus at (8,0) and directrix x=-8      Log On


   

Question 1173278: Find the equation of the parabola with focus at (8,0) and directrix x=-8
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The focus is to the right of the directrix, so the parabola opens to the right. The equation is

%28x-h%29+=+%281%2F%284p%29%29%28y-k%29%5E2

where the vertex is (h,k) and p is the directed distance (i.e., can be negative) from the directrix to the vertex and from the vertex to the focus.

The vertex is halfway between the directrix and focus, so the vertex is (h,k) = (0,0). That makes p = 8.

Plug in the values of h, k, and p:

%28x-0%29+=+%281%2F%284%288%29%29%29%28y-0%29%5E2

x+=+%281%2F32%29y%5E2