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# Hyperbolas and Completing the Square : Vertices, Foci and Asymptotes

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Completing the square problems: HYPERBOLAS-
Find the center, vertices, foci, and asymptotes of the hyperbola. Please give the equation in standard form, i.e. (x-h)^2/a^2 - (y-k)^2/b^2=1 or other way around.
15)
? 9x^2-y^2-36x-6y+18=0

Answer: Center (2,-3)
Vertices (3,-3), (1,-3)
Foci: (2+ or &#8730;10, -3)
Asymptotes: (y=-3 + or - 3(x+2).
17)
? x^2-9y^2+2x-54y-80=0
Answer: The graph of this equation is two lines intersecting at (-1,-3)? Is that all?
19)
? 2x^2-3y^2=6
Center: (0, 0)
Vertices: (+ or - &#8730;3, 0)
Foci: (+ or - &#8730;5, 0)

21)
? 9y^2-x^2+2x+54y+62=0
Center: (1,-3)
Vertices: (1,-3 + or - &#8730;2)
Foci: (1, -3 + or - (2&#8730;5) )
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##### Solution Summary

Hyperbolas, Completing the Square, Vertices, Foci and Asymptotes are investigated. The solution is detailed and well presented.

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