Step 1:

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The hyperbola equation is $\"\"$ .

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The y - term is positive then the hyperbola is horizontal.

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

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Where $\"\"$ is the center of the hyperbola, $\"\"$ is the length of the semi major axis and $\"\"$ is the semi minor axis.

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Compare $\"\"$ with standard form of vertical hyperbola.

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

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$\"\"$

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$\"\"$

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Find length of the semi major axis.

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$\"\"$

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Find the length of the semi minor axis.

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$\"\"$ $\"\"$

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Step 2:

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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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The asymptotes are

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$\"\"$

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The asymptotes are $\"\"$ .

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Step 3:

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Plot the center point $\"\"$ .

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Plot the focus points $\"\"$ and vertex points $\"\"$ .

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Draw the asymptotes are $\"\"$ .

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Sketch the hyperbola.

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$\"\"$

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Solution:

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

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The vertices are $\"\"$ .

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The foci are $\"\"$ .

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The asymptotes are $\"\"$ .