Write the Equation of the Hyperbola in Standard Form $$- 144 x ^ { 2 } + 9 y ^ { 2 } + 384 x + 36 y - 1,516 = 0$$

question 38

Multiple Choice

Write the equation of the hyperbola in standard form. Identify the center and vertices.
- $$- 144 x ^ { 2 } + 9 y ^ { 2 } + 384 x + 36 y - 1,516 = 0$$

• A) \(\frac { ( y - 2 ) ^ { 2 } } { 144 } - \frac { \left( x + \frac { 4 } { 3 } \right) ^ { 2 } } { 9 } = 0\)
• center: \(\left( - \frac { 4 } { 3 } , 2 \right)\)
• vertices: \(\left( - \frac { 4 } { 3 } , 14 \right)\) and \(\left( - \frac { 4 } { 3 } , - 10 \right)\)
• B) \(\frac { ( y + 2 ) ^ { 2 } } { 144 } - \frac { \left( x - \frac { 4 } { 3 } \right) ^ { 2 } } { 9 } = 0\)
• center: \(\left( \frac { 4 } { 3 } , - 2 \right)\)
• vertices: \(\left( \frac { 4 } { 3 } , 10 \right)\) and \(\left( \frac { 4 } { 3 } , - 14 \right)\)
• C) \(\frac { ( y + 2 ) ^ { 2 } } { 144 } - \frac { \left( x - \frac { 4 } { 3 } \right) ^ { 2 } } { 9 } = 1\)
• center: \(\left( \frac { 4 } { 3 } , - 2 \right)\)
• vertices: \(\left( \frac { 4 } { 3 } , 10 \right)\) and \(\left( \frac { 4 } { 3 } , - 14 \right)\)
• D) \(\frac { ( y - 2 ) ^ { 2 } } { 144 } - \frac { \left( x + \frac { 4 } { 3 } \right) ^ { 2 } } { 9 } = 1\)
• center: \(\left( - \frac { 4 } { 3 } , 2 \right)\)
• vertices: \(\left( - \frac { 4 } { 3 } , 14 \right)\) and \(\left( - \frac { 4 } { 3 } , - 10 \right)\)

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