Write the Equation of the Ellipse in Standard Form $$4 x ^ { 2 } + 9 y ^ { 2 } + 12 x - 108 y + 297 = 0$$

question 33

Multiple Choice

Write the equation of the ellipse in standard form. Identify the center and foci.
- $$4 x ^ { 2 } + 9 y ^ { 2 } + 12 x - 108 y + 297 = 0$$

• A) \(\frac { \left( x + \frac { 3 } { 2 } \right) ^ { 2 } } { 9 } + \frac { ( y - 6 ) ^ { 2 } } { 4 } = 1\)
• center: \(\left( - \frac { 3 } { 2 } , 6 \right)\)
• foci: \(\left( - \frac { 3 } { 2 } - \sqrt { 5 } , 6 \right) , \left( - \frac { 3 } { 2 } + \sqrt { 5 } , 6 \right)\)
• B) \(\frac { \left( x + \frac { 3 } { 2 } \right) ^ { 2 } } { 9 } + \frac { ( y - 6 ) ^ { 2 } } { 4 } = 1\)
• center: \(\left( - \frac { 3 } { 2 } , 6 \right)\)
• foci: \(\left( - \frac { 9 } { 2 } , 6 \right) , \left( \frac { 3 } { 2 } , 6 \right)\)
• C) \(\frac { \left( x + \frac { 3 } { 2 } \right) ^ { 2 } } { 9 } + \frac { ( y - 6 ) ^ { 2 } } { 4 } = 1\)
• center: \(\left( \frac { 3 } { 2 } , - 6 \right)\)
• foci: \(\left( \frac { 3 } { 2 } - \sqrt { 5 } , - 6 \right) , \left( \frac { 3 } { 2 } + \sqrt { 5 } , - 6 \right)\)
• foci: \(\left( \frac { 3 } { 2 } - \sqrt { 5 } , - 6 \right) , \left( \frac { 3 } { 2 } + \sqrt { 5 } , - 6 \right)\)
• D) \(\frac { \left( x - \frac { 3 } { 2 } \right) ^ { 2 } } { 9 } + \frac { ( y + 6 ) ^ { 2 } } { 4 } = 1\)
• center: \(\left( \frac { 3 } { 2 } , - 6 \right)\)
• foci: \(\left( \frac { 3 } { 2 } - \sqrt { 5 } , - 6 \right) , \left( \frac { 3 } { 2 } + \sqrt { 5 } , - 6 \right)\)

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