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

question 45

Multiple Choice

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $25 y ^ { 2 } - 16 x ^ { 2 } = 400$

• A) center at \( (0,0) \)
• transverse axis is \( x \)-axis
• vertices: \( (-5,0),(5,0) \)
• foci: \( (-\sqrt{41}, 0),(\sqrt{41}, 0) \)
• asymptotes of \( y=-\frac{4}{5} \) and \( y=\frac{4}{5} \)
• B) center at \( (0,0) \)
• transverse axis is \( x \)-axis
• vertices: \( (-4,0),(4,0) \)
• foci: \( (-5,0),(5,0) \)
• asymptotes of \( y=-\frac{4}{5} \) and \( y=\frac{4}{5} \)
• C)center at \( (0,0) \)
• transverse axis is \( \mathrm{y} \)-axis
• vertices: \( (0,-4),(0,4) \)
• foci: \( (-\sqrt{41}, 0),(\sqrt{41}, 0) \)
• asymptotes of \( y=-\frac{4}{5} \) and \( y=\frac{4}{5} \)
• D)center at \( (0,0) \)
• transverse axis is \( y \)-axis
• vertices at \( (0,-4) \) and \( (0,4) \)
• foci at \( (0,-\sqrt{41}) \) and \( (0, \sqrt{41}) \)
• asymptotes of \( y=-\frac{4}{5} \) and \( y=\frac{4}{5} \)

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