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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.
- 49x23649y264=1\frac { 49 x ^ { 2 } } { 36 } - \frac { 49 y ^ { 2 } } { 64 } = 1


A) vertices: (76,0) ,(76,0) \left( \frac { 7 } { 6 } , 0 \right) , \left( - \frac { 7 } { 6 } , 0 \right)
foci: (107,0) ,(107,0) \left( \frac { 10 } { 7 } , 0 \right) , \left( - \frac { 10 } { 7 } , 0 \right)
asymptotes: y=34xy = \frac { 3 } { 4 } x and y=34xy = - \frac { 3 } { 4 } x
B) vertices: (76,0) ,(76,0) \left( \frac { 7 } { 6 } , 0 \right) , \left( - \frac { 7 } { 6 } , 0 \right)
foci: (107,0) ,(107,0) \left( \frac { 10 } { 7 } , 0 \right) , \left( - \frac { 10 } { 7 } , 0 \right)
asymptotes: y=43xy = \frac { 4 } { 3 } x and y=43xy = - \frac { 4 } { 3 } x
C) vertices: (76,0) ,(76,0) \left( \frac { 7 } { 6 } , 0 \right) , \left( - \frac { 7 } { 6 } , 0 \right)
foci: (702,401,0) ,(702,401,0) \left( \frac { 70 } { 2,401 } , 0 \right) , \left( - \frac { 70 } { 2,401 } , 0 \right)
asymptotes: y=43xy = \frac { 4 } { 3 } x and y=43xy = - \frac { 4 } { 3 } x
D) vertices: (78,0) ,(78,0) \left( \frac { 7 } { 8 } , 0 \right) , \left( - \frac { 7 } { 8 } , 0 \right)
foci: (107,0) ,107,0) \left. \left( \frac { 10 } { 7 } , 0 \right) , - \frac { 10 } { 7 } , 0 \right)
asymptotes: y=43xy = \frac { 4 } { 3 } x and y=43xy = - \frac { 4 } { 3 } x

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