Question 1175595: Write the standard form of the equation of the parabola with focus at (-2,5) and directrix at x=4.
Answer by greenestamps(13200)   (Show Source):
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Focus at (-2,5) and directrix at x=4 means the parabola opens to the left.
The vertex is on the axis of symmetry, halfway between the focus and directrix. Halfway between -2 and 4 is 1, so the vertex is (1,5).
The vertex form of the equation, with vertex (h,k), is
 ,
or
In that form of the equation, p is the directed distance (i.e., can be negative) from the directrix to the vertex, and from the vertex to the focus. For the given parabola, then, p is -3.
So we have (h,k) = (1,5) and p = -3; the vertex form of the equation is
You can do the conversion of the equation to standard form.
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