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

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 √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 - √3, 0)

Foci: (+ or - √5, 0)

21)

? 9y^2-x^2+2x+54y+62=0

Center: (1,-3)

Vertices: (1,-3 + or - √2)

Foci: (1, -3 + or - (2√5) )

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https://brainmass.com/math/algebra/hyperbolas-completing-square-vertices-foci-asymptotes-57600

#### Solution Summary

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