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Write an equation of a parabola that has a directx of y= -5 and a focus at (2,-1)?

I'm guessing focus here means the vertex

$$ Y = a(x-h)^2 + k$$ $$-5 = a(x-2)^2 -1$$ $$-5 + 1 = a(x-2)^2$$

If i take the -4 to the other side than it would be $$0=a(x-2)^2+4$$ and the given answer choice doesn't have any of this How would i solve this?

MATH ASKER
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1 Answers1

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The focus is not the vertex. The vertex is the midpoint of the line segment connecting the focus with the directrix and perpendicular to the directrix. Geometrically, a parabola is the set of all points that are equidistant from a fixed point called the focus and a fixed line called the directrix.

B.H.
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