Write the Equation of the Ellipse in Standard Form $$36 x ^ { 2 } + 25 y ^ { 2 } + 100 y + 99 = 0$$

question 90

Multiple Choice

Write the equation of the ellipse in standard form. Identify the vertices and foci.
- $$36 x ^ { 2 } + 25 y ^ { 2 } + 100 y + 99 = 0$$

• A) \(\frac { x ^ { 2 } } { \frac { 1 } { 36 } } + \frac { ( y + 2 ) ^ { 2 } } { \frac { 1 } { 25 } } = 1\)
• vertices: \(\left( - \frac { 9 } { 5 } , 0 \right) , \left( - \frac { 11 } { 5 } , 0 \right)\)
• foci: \(\left( 2 + \frac { \sqrt { 11 } } { 30 } , 0 \right) , \left( 2 - \frac { \sqrt { 11 } } { 30 } , 0 \right)\)
• B) \(\frac { x ^ { 2 } } { \frac { 1 } { 36 } } + \frac { ( y + 2 ) ^ { 2 } } { \frac { 1 } { 25 } } = 1\)
• vertices: \(\left( 0 , - \frac { 9 } { 5 } \right) , \left( 0 , - \frac { 11 } { 5 } \right)\)
• foci: \(\left( 0,2 + \frac { \sqrt { 11 } } { 30 } \right) , \left( 0,2 - \frac { \sqrt { 11 } } { 30 } \right)\)
• C) \(36 x ^ { 2 } + 25 ( y + 2 ) ^ { 2 } = 1\)
• vertices: \(( 36 , - 2 ) , ( - 36 , - 2 )\)
• foci: \(\left( 0,2 + \frac { \sqrt { 11 } } { 30 } \right) , \left( 0,2 - \frac { \sqrt { 11 } } { 30 } \right)\)
• D) \(36 x ^ { 2 } + 25 ( y + 2 ) ^ { 2 } = 1\)
• vertices: \(\left( 0 , - \frac { 9 } { 5 } \right) , \left( 0 , - \frac { 11 } { 5 } \right)\)
• foci: \(\left( 0,2 + \frac { \sqrt { 11 } } { 30 } \right) , \left( 0,2 - \frac { \sqrt { 11 } } { 30 } \right)\)

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