Find the Center, Foci, and Vertices of the Ellipse $$2 x ^ { 2 } + 5 y ^ { 2 } - 12 x + 60 y + 188 = 0$$

question 1

Multiple Choice

Find the center, foci, and vertices of the ellipse.
- $$2 x ^ { 2 } + 5 y ^ { 2 } - 12 x + 60 y + 188 = 0$$

• A) \(\frac { ( x - 3 ) ^ { 2 } } { 2 } + \frac { ( y + 6 ) ^ { 2 } } { 5 } = 1\)
• center: \(( - 3,6 )\); foci: \(( - 1.3,6 ) , ( - 4.7,6 )\); vertices: \(( - 5.2,6 ) , ( - 0.8,6 )\)
• B) \(\frac { ( x - 3 ) ^ { 2 } } { 5 } + \frac { ( y + 6 ) ^ { 2 } } { 2 } = 1\)
• center: \(( 3 , - 6 )\); foci: \(( 4.7 , - 6 ) , ( 1.3 , - 6 )\); vertices: \(( 5.2 , - 6 ) , ( 0.8 , - 6 )\)
• C) \(\frac { ( x - 3 ) ^ { 2 } } { 5 } + \frac { ( y + 6 ) ^ { 2 } } { 2 } = 1\)
• center: \(( - 3,6 )\); foci: \(( - 1.3,6 ) , ( - 4.7,6 )\); vertices: \(( - 5.2,6 ) , ( - 0.8,6 )\)
• D) \(\frac { ( x - 3 ) ^ { 2 } } { 2 } + \frac { ( y + 6 ) ^ { 2 } } { 5 } = 1\)
• center: \(( 3 , - 6 )\); foci: \(( 4.7 , - 6 ) , ( 1.3 , - 6 )\); vertices: \(( 5.2 , - 6 ) , ( 0.8 , - 6 )\)

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