Identify the Vertices and the Foci, and Write Equations for the Asymptotes

question 87

Multiple Choice

Identify the vertices and the foci, and write equations for the asymptotes.
- $\frac { 49 x ^ { 2 } } { 36 } - \frac { 49 y ^ { 2 } } { 64 } = 1$

• A) vertices: \(\left( \frac { 7 } { 6 } , 0 \right) , \left( - \frac { 7 } { 6 } , 0 \right)\)
• foci: \(\left( \frac { 10 } { 7 } , 0 \right) , \left( - \frac { 10 } { 7 } , 0 \right)\)
• asymptotes: \(y = \frac { 3 } { 4 } x\) and \(y = - \frac { 3 } { 4 } x\)
• B) vertices: \(\left( \frac { 7 } { 6 } , 0 \right) , \left( - \frac { 7 } { 6 } , 0 \right)\)
• foci: \(\left( \frac { 10 } { 7 } , 0 \right) , \left( - \frac { 10 } { 7 } , 0 \right)\)
• asymptotes: \(y = \frac { 4 } { 3 } x\) and \(y = - \frac { 4 } { 3 } x\)
• C) vertices: \(\left( \frac { 7 } { 6 } , 0 \right) , \left( - \frac { 7 } { 6 } , 0 \right)\)
• foci: \(\left( \frac { 70 } { 2,401 } , 0 \right) , \left( - \frac { 70 } { 2,401 } , 0 \right)\)
• asymptotes: \(y = \frac { 4 } { 3 } x\) and \(y = - \frac { 4 } { 3 } x\)
• D) vertices: \(\left( \frac { 7 } { 8 } , 0 \right) , \left( - \frac { 7 } { 8 } , 0 \right)\)
• foci: \(\left. \left( \frac { 10 } { 7 } , 0 \right) , - \frac { 10 } { 7 } , 0 \right)\)
• asymptotes: \(y = \frac { 4 } { 3 } x\) and \(y = - \frac { 4 } { 3 } x\)

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