3 years ago

Find the equation for a parabola with its focus at (0, 3) and a directrix of y = -3.

Mathematics

1 answer:

GrogVix [38]3 years ago

4 0

Answer:

y = (1/12)x^2

Step-by-step explanation:

The vertex of this parabola is halfway between (0, 3) and the directrix, y = -3; that is, it's at (0, 0).

The applicable equation for this vertical parabola is 4py = x^2, where p is the distance between the vertex and the focus. Here that distance is p = 3.

Thus, 4py = x^2 becomes 4(3)y = x^2, or 12y = x^2, or y = (1/12)x^2.

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