$\"\"$

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The equations of hyperabolas are $\"\"$ and $\"\"$ .

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Consider hyperbola equation is $\"\"$ .

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

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

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Compare the hyperbola equatrion with standard form.

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Here $\"\"$ , $\"\"$ and $\"\"$ .

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

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

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$\"\"$ .

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$\"\"$

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Consider hyperbola equation is $\"\"$ .

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

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

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

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

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Compare the hyperbola equatrion with standard form.

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Here $\"\"$ , $\"\"$ and $\"\"$ .

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

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

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$\"\"$ .

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Two hyperbolas that have the same set of asymptotes are called conjugate.

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Therefore, the two hyperbolas are conjugate.

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$\"\"$

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Graph:

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Graph the hyperbolas $\"\"$ and $\"\"$ . $\"\"$

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$\"\"$

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Asymptotes of $\"\"$ are $\"\"$ .

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Asymptotes of $\"\"$ are $\"\"$ .

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The two hyperbolas are conjugate.

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Graph of the two hyperbolas is

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$\"\"$ .