A parabola, with its vertex at the origin, has a directrix at y = 3.Which statements about the parabola are true? Select two options.The focus is located at (0,–3).The parabola opens to the left. The p value can be determined by computing 4(3).The parabola can be represented by the equation x2 = –12y.The parabola can be represented by the equation y2 = 12x.
Answer
A
The focus is located at (0,–3).
B
The parabola opens to the left.
C
The p value can be determined by computing 4(3).
D
The parabola can be represented by the equation x2 = –12y.
E
The parabola can be represented by the equation y2 = 12x.
Explanation
For a vertical parabola with vertex at the origin, the directrix is y = -p and the focus is (0, p). Since the directrix is y = 3, p = -3, so the focus is (0, -3). Using x² = 4py gives x² = 4(-3)y = -12y, so the parabola opens downward and is represented by x² = -12y.
AI-written and checked against the verified answer.