SOLUTION: Find the equation of the parabola with vertex at the origin, focus at (3m, 0) and directrix with equation x=–3m.

Algebra ->  Points-lines-and-rays -> SOLUTION: Find the equation of the parabola with vertex at the origin, focus at (3m, 0) and directrix with equation x=–3m.       Log On


   

Question 1127348: Find the equation of the parabola with vertex at the origin, focus at (3m, 0) and directrix with equation x=–3m.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Points (x,y) so that distance from focus equals distance from directrix

sqrt%28%28x-3m%29%5E2%2B%28y-0%29%5E2%29=sqrt%28%28x-%28-3m%29%29%5E2%2B%28y-y%29%5E2%29
-
%28x-3m%29%5E2%2By%5E2=%28x%2B3m%29%5E2
y%5E2=%28x%2B3m%29%5E2-%28x-3m%29%5E2
y%5E2=x%5E2%2B6mx%2B9m%5E2-%28x%5E2-6mx%2B9m%5E2%29
y%5E2=x%5E2%2B6mx%2B9m%5E2-x%5E2%2B6mx-9m%5E2
highlight%28y%5E2=12mx%29
OR
x=%281%2F%2812m%29%29y%5E2