$\"\"$

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The hyperbola equation is $\"\"$ .

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Rewritr the equation as $\"\"$ .

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

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Where the hyperbola is transverse about $\"\"$ -axis and $\"\"$ is the center.

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$\"\"$ is the distance between center and vertex.

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$\"\"$ is the distance between center and focus and $\"\"$ .

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

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

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Asymptotes of the hyperbola are $\"\"$ .

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$\"\"$

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The hyperbola equation is $\"\"$ .

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Comapre the equation with general form of hyperbola.

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

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

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

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$ .

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

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$ .

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The foci is at $\"\"$ and $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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The vertices are at $\"\"$ and $\"\"$ .

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Substitute $\"\"$ and $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$ .

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The asymptotes are $\"\"$ and $\"\"$ .

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$\"\"$

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Form the rectangle with points $\"\"$ and $\"\"$ .

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$\"\"$ are the vertices points.

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Find $\"\"$ .

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

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Graph : Graph of the hyperbola is

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$\"\"$

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$\"\"$

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

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The hyperbola is transverse about $\"\"$ .

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The vertices are at $\"\"$ and $\"\"$ .

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The foci is at $\"\"$ and $\"\"$ .

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The asymptotes are $\"\"$ and $\"\"$ .

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Graph of the hyperbola is

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$\"\"$ .