Find the Center, Transverse Axis, Vertices, Foci, and Asymptotes of the Hyperbola

question 187

Multiple Choice

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $$\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 4 } = 1$$

• A) center at \( (0,0) \)
• transverse axis is \( \mathrm{x} \)-axis
• vertices at \( (-11,0) \) and \( (11,0) \)
• foci at \( (-\sqrt{137}, 0) \) and \( (\sqrt{137}, 0) \)
• asymptotes of \( y=-\frac{11}{4} \) and \( y=\frac{11}{4} \)
• B)center at \( (0,0) \)
• transverse axis is \( \mathrm{y} \)-axis
• vertices at \( (0,-4) \) and \( (0,4) \)
• foci at \( (-\sqrt{137}, 0) \) and \( (\sqrt{137}, 0) \)
• asymptotes of \( y=-\frac{11}{4} \) and \( y=\frac{11}{4} \)
• C) \(\begin{array}{l}
• \text { center at }(0,0) \\
• \text { transverse axis is } x \text {-axis } \\
• \text { vertices at }(-4,0) \text { and }(4,0) \\
• \text { foci at }(-11,0) \text { and }(11,0) \\
• \text { asymptotes of } y=-\frac{11}{4} \text { and } y=\frac{11}{4}
• \end{array}\)
• D) \(\begin{array}{l}
• \text { center at }(0,0) \\
• \text { transverse axis is x-axis } \\
• \text { vertices at }(-4,0) \text { and }(4,0) \\
• \text { foci at }(-\sqrt{137}, 0) \text { and }(\sqrt{137}, 0) \\
• \text { asymptotes of } y=-\frac{11}{4} \text { and } y=\frac{11}{4}
• \end{array}\)

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