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AssignmentMultiple Choice

Conic Sections: Parabolas

Question 2 • TX-Pre-Calculus

Write the equation of a parabola with the focus at (3, 0) and the directrix at x = –3.

Answer
A
x2 = –3y
B
y2 = –3x
C
x2 = 12y
D
y2 = 12x

Explanation

The focus is (3, 0) and the directrix is x = −3, so the parabola opens to the right along the x-axis. The vertex lies halfway between them at (0, 0), making the focal distance p = 3. Using the standard form y² = 4px gives y² = 4(3)x = 12x, which is choice D.

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