$\"\"$

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The hyperbola equation is $\"\"$ .

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Consider the vertical line of the hyperbola is $\"\"$ .

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Where $\"\"$ and the focus of the hyperbola is $\"\"$ .

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The area enclosed by the hyperbola is $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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Apply the formula : $\"\"$ .

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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 $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The area enclosed by the hyperbola is $\"\"$ .

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$\"\"$

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The area enclosed by the hyperbola is $\"\"$ .