Question

PLS HELP...ASAP
Which is the equation of a parabola with a directrix at y = -3 and a focus at (-2, 3).
y= 1/12(x - 2)²
y=1/12(x+2)²
y=-1/12(x + 2)²
y=-1/12(x-2)²
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Answer 1

Answer:

Step-by-step explanation:

If you plot the directrix, which is a horizontal line, then you plot the focus, which is above the directrix, you know that this parabola opens upwards (meaning it is positive), since a parabola always wraps itself around the focus, directed away from the directrix.  The standard form of this type of parabola is

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

where h and k are the coordinates of the vertex.  We were not given those coordinates, but we SHOULD know by now that the vertex is directly between the focus and the directrix, on the same axis of symmetry as the focus is.  So the vertex is located at (-2, 0).  Therefore, h = -2, k = 0.

P is defined as the distance between the vertex and the focus, or the vertex and the directrix, since they are the same.  Our p is 3 units.

Filling in our equation then gives us

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

$(x+2)^2=12y$ and

$\frac{1}{12}(x+2)^2=y$

The second choice is the one you want.