Write the Equation of the Ellipse in Standard Form $$x ^ { 2 } + 81 y ^ { 2 } - 14 x - 32 = 0$$

question 80

Multiple Choice

Write the equation of the ellipse in standard form. Identify the vertices and foci.
- $$x ^ { 2 } + 81 y ^ { 2 } - 14 x - 32 = 0$$

• A) \(\frac { ( x + 7 ) ^ { 2 } } { 81 } + y ^ { 2 } = 1\)
• vertices: \(( - 16,0 ) , ( 2,0 )\)
• foci \(( - 7 - 4 \sqrt { 5 } , 0 ) , ( - 7 + 4 \sqrt { 5 } , 0 )\)
• B) \(x ^ { 2 } + \frac { ( y + 7 ) ^ { 2 } } { 81 } = 1\)
• vertices: \(( 0 , - 16 ) , ( 0,2 )\)
• foci \(( 0 , - 7 - 4 \sqrt { 5 } ) , ( 0 , - 7 + 4 \sqrt { 5 } )\)
• C) \(\frac { ( x - 7 ) ^ { 2 } } { 81 } + y ^ { 2 } = 1\)
• vertices: \(( - 2,0 ) , ( 16,0 )\)
• foci \(( 7 - 4 \sqrt { 5 } , 0 ) , ( 7 + 4 \sqrt { 5 } , 0 )\)
• D) \(x ^ { 2 } + \frac { ( y - 7 ) ^ { 2 } } { 81 } = 1\)
• vertices: \(( 0 , - 16 ) , ( 0,2 )\)
• foci \(( 0,7 - 4 \sqrt { 5 } ) , ( 0,7 + 4 \sqrt { 5 } )\)