Find the Center, Foci, and Vertices of the Ellipse $16 x ^ { 2 } + y ^ { 2 } - 256 x + 1,008 = 0$

question 185

Multiple Choice

Find the center, foci, and vertices of the ellipse.
- $16 x ^ { 2 } + y ^ { 2 } - 256 x + 1,008 = 0$

• A) \(( x - 2 ) ^ { 2 } + \frac { y ^ { 2 } } { 64 } = 1\)
• center: \(( 2,0 )\); foci: \(( 2,3 \sqrt { 7 } ) , ( 2 , - 3 \sqrt { 7 } )\); vertices:( 2,\(8 ), ( 2 , - 8 )\)
• B) \(( x - 8 ) ^ { 2 } + \frac { y ^ { 2 } } { 4 } = 1\)
• center: \(( 8,0 )\); foci: \(( 8 , \sqrt { 3 } ) , ( 8 , - \sqrt { 3 } )\); vertices: \(( 8,2 ) , ( 8 , - 2 )\)
• C) \(\frac { x ^ { 2 } } { 64 } + ( y - 2 ) ^ { 2 } = 1\)
• center: \(( 2,0 )\); foci: \(( 2,3 \sqrt { 7 } ) , ( 2 , - 3 \sqrt { 7 } )\); vertices: \(( 2,8 ) , ( 2 , - 8 )\)
• D) \(\frac { x ^ { 2 } } { 4 } + ( y - 8 ) ^ { 2 } = 1\)
• center: \(( 8,0 )\); foci: \(( 8 , \sqrt { 3 } ) , ( 8 , - 3 \sqrt { 7 } )\); vertices: \(( 8,2 )\), \(( 8 , - 2 )\)

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