SOLUTION: Find the equation for a parabola with its focus at (5, 0) and a directrix of x = -5

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the equation for a parabola with its focus at (5, 0) and a directrix of x = -5      Log On


   

Question 756237: Find the equation for a parabola with its focus at (5, 0) and a directrix of x = -5
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The way the focus and directrix are positioned, this parabola has a minimum. The vertex is directly in the exact middle of focus and directrix, so vertex is (0,0). Without going to derivation process for a parabola equation, you can use x%5E2=4py, where p is the focal length, same as distance from vertex to the closest point on the directrix.

In your question, p=5, and since the parabola has a minimum, the coefficient on x%5E2 is positive (when written in the form y=something...).

4py=x%5E2
y=%281%2F%284p%29%29x%5E2
and knowing p=5
y=%281%2F%284%2A5%29%29x%5E2
highlight%28y=%281%2F20%29x%5E2%29

graph%28300%2C300%2C-15%2C15%2C-15%2C15%2C%281%2F20%29x%5E2%29