Find the equation of the parabola determine by the given information.
Focus (6,0), directrix x = -6
Solution
First, notice that since the directrix is a vertical line, the parabola will open either to the left or to the right, not up or down. Since the directris is to the left of the focus, and a parabola always opens aways from its directris, this parabola will open to the right.
The vertex will be halfway between the focus and the directrix. It will have the same y-coordinate as the y-coordinate of the focus.
The vertex of the parabola is (
), which simplifies to (0,0).
The parabola with directrix x = -p and vertex (0,0) will have the equation 
= 4px.
Since the directrix of this parabola is x = -6, p = 6.
The equation of the parabola with directrix x = -6 and focus (6,0) is = 4*6x , which simplifies to = 24x.