Step 1:

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The hyperbola equation is $\"\"$ .

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Convert the equation in standard form of hyperbola.

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$\"\"$

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To change the expressions $\"\"$ and $\"\"$ into a perfect square trinomial,

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add (half the x coefficient)² and add (half the y coefficient)² to each side of the equation.

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Compare it to standard form of vertical hyperbola is $\"\"$ .

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Where $\"\"$ is the center of the hyperbola $\"\"$ .

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The center of the hyperbola is $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$ .

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$\"\"$

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The standard form of hyperbola is $\"\"$ .

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foci is $\"\"$ , vertices are $\"\"$ and asymptotes are $\"\"$ .

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The hyperbola equation is $\"\"$ .

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foci are $\"\"$ .

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Vertices are $\"\"$ .

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Vertices are $\"\"$ .

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The asymptotes are $\"\"$ .

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Step 3:

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Graph the hyperbola.

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Graph the equation $\"\"$ .

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Plot the center point $\"\"$ .

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Plot the focus points $\"\"$ .

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Plot the vertex points $\"\"$ .

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Draw the asymptotes are $\"\"$ .

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$\"\"$

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Solution:

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Foci are $\"\"$ .

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Vertices are $\"\"$ .

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The asymptotes are $\"\"$ .