Problem 1082

Find the equation of the parabola determine by the given information.

Focus (6,0), directrix x = -6




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 directrix is to the left of the focus, and a parabola always opens away from its directrix, 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 (\frac{6+(-6)}{2},0), which simplifies to (0,0).

The parabola with directrix x = -p and vertex (0,0) will have the equation y2 = 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  y2 = 4*6x, which simplify to y2 = 24x.




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