Question

The equation of a parabola is (y + 2)^2 = 12 (x -5). What is the equation of the directrix of the parabola? Enter your answer in the box. Correct answers only!!!!

Answer 1

`\boxed{x=2}`

Explanation:

The equation of a parabola with vertex (h, k) and directrix-to-vertex distance p is given by ...

(y -k)^2 = 4p(x -h)

The directrix is the line x = (h -p)

Here, we have the vertex at x=5. The distance from the directrix satisfies ...

12 = 4p

12/4 = p = 3

So, the directrix is at x = 5 - 3, or x = 2.

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The graph shows the given parabola along with the focus and directrix. The dashed lines are intended to show that each of those is in the right place, as the distance from any point on the parabola is the same to the focus and the directrix.