A parabola, with its vertex at the origin, has a directrix at y = 3. Which statements about the parabola are true? Select two op

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A parabola, with its vertex at the origin, has a directrix at y = 3. Which statements about the parabola are true? Select two op

tions.
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.

Mathematics

2 answers:

Svet_ta [9.5K] · Answer 1 · 2026-03-20T14:48:00+03:00

To comprehensively address these queries, graphing the vertex alongside the directrix indicates that the vertex lies below the directrix. Since a parabola opens away from the directrix, it must be inverted, resembling the equation format

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

. The 'p' component in this context refers to the distance, specifically the gap from the vertex to either the directrix or the focus. The vertex is centrally positioned between these two points, indicating the focus is located 3 units below the vertex (since the directrix is 3 units above it). Thus, we conclude that p = 3.

Substituting h and k, both being (0, 0), into the equation gives:

$4(3)(y-0)=-(x-0)^2$ resulting in