Find the Center, Foci, and Vertices of the Ellipse $$25 x ^ { 2 } + y ^ { 2 } - 450 x + 2000 = 0$$

question 20

Multiple Choice

Find the center, foci, and vertices of the ellipse.
- $$25 x ^ { 2 } + y ^ { 2 } - 450 x + 2000 = 0$$

• A) \(( x - 9 ) ^ { 2 } + \frac { y ^ { 2 } } { 25 } = 1\)
• center: \(( 9,0 )\); foci: \(( 9,2 \sqrt { 6 } ) , ( 9 , - 2 \sqrt { 6 } )\); vertices: \(( 9,5 ) , ( 9 , - 5 )\)
• B) \(\frac { x ^ { 2 } } { 25 } + ( y - 9 ) ^ { 2 } = 1\)
• center: \(( 9,0 )\); foci: \(( 9,2 \sqrt { 6 } ) , ( 9 , - 2 \sqrt { 6 } )\); vertices: \(( 9,5 ) , ( 9 , - 5 )\)
• C) \(\frac { x ^ { 2 } } { 81 } + ( y - 5 ) ^ { 2 } = 1\)
• center: \(( 5,0 )\); foci: \(( 5,4 \sqrt { 5 } ) , ( 5 , - 2 \sqrt { 6 } )\); vertices: \(( 5,9 )\), \(( 5 , - 9 )\)
• D) \(( x - 5 ) ^ { 2 } + \frac { y ^ { 2 } } { 81 } = 1\)
• center: \(( 5,0 )\); foci: \(( 5,4 \sqrt { 5 } ) , ( 5 , - 4 \sqrt { 5 } )\); vertices: \(( 5,9 ) , ( 5 , - 9 )\)

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