117979
AssignmentMultiple Choice

Parabolas

Question 117979 • *CR CCSS Math 2 S2 [M2960OX]

If the directrix of a parabola is the horizontal line y = 3, what is true of the parabola?

Answer
A
The focus is at (0, 3), and the equation for the parabola is y2 = 12x.
B
The focus is at (0, –3), and the equation for the parabola is x2 = –12y.
C
The focus is at (3, 0), and the equation for the parabola is x2 = 12y.
D
The focus is at (–3, 0), and the equation for the parabola is y2 = –12x.

Explanation

For a vertical parabola with vertex at the origin, the equation is x² = 4py, its focus is (0, p), and its directrix is y = −p. Setting the directrix equal to y = 3 gives p = −3, so the focus is (0, −3) and the equation is x² = −12y. Therefore, choice B is correct.

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