$\"\"$

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Observe the graph:

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The hyperbola is horizontal.

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Standard form of hyperbola is $\"\"$ , where $\"\"$ is center.

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Vertices: $\"\"$ .

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Foci: $\"\"$ .

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Asymptotes: $\"\"$ .

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$\"\"$ .

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The center of the hyperbola located at $\"\"$ .

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The vertices of the hyperbola is $\"\"$ .

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Therefore, $\"\"$ and $\"\"$ .

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$\"\"$

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Find the value of $\"\"$ .

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The point $\"\"$ is lies on the hyperbola.

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By the definition of the hyperbola, the absolute value of the differences from any point on the hyperbola to the foci is constant.

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$\"\"$ .

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Let $\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$

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Substitute the corresponding values in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Square on both sides.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Divide each side by $\"\"$ .

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$\"\"$

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Square on both sides.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute the values $\"\"$ and $\"\"$ in standard form.

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$\"\"$

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$\"\"$ .

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$\"\"$

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The hyperbola equation is $\"\"$ .