Find the Asymptotes of the Hyperbola $\frac { y ^ { 2 } } { \frac { 25 } { 9 } } - \frac { x ^ { 2 } } { 16 } = 1$

question 4

Multiple Choice

Find the asymptotes of the hyperbola.
-A satellite following the hyperbolic path shown in the picture turns rapidly at (0, 4) and then moves closer and closer to the line y = 125 x as it gets farther from the tracking station at the origin. Find the equation that Describes the path of the rocket if the center of the hyperbola is at (0, 0) .

• A) \(\frac { y ^ { 2 } } { \frac { 25 } { 9 } } - \frac { x ^ { 2 } } { 16 } = 1\)
• B) \(\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { \left( \frac { 36 } { 5 } \right) ^ { 2 } } = 1\)
• C) \(\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { \frac { 25 } { 9 } } = 1\)
• D) \(\frac { x ^ { 2 } } { \left( \frac { 36 } { 5 } \right) ^ { 2 } } - \frac { y ^ { 2 } } { 16 } = 1\)

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