Write the Equation of the Ellipse in Standard Form $$25 x ^ { 2 } + y ^ { 2 } + 14 y + 24 = 0$$

question 73

Multiple Choice

Write the equation of the ellipse in standard form. Identify the vertices and foci.
- $$25 x ^ { 2 } + y ^ { 2 } + 14 y + 24 = 0$$

• A) \(x ^ { 2 } + \frac { ( y + 7 ) ^ { 2 } } { 25 } = 1\)
• vertices: \(( 0 , - 12 ) , ( 0 , - 2 )\)
• foci \(( 0 , - 7 - 2 \sqrt { 6 } ) , ( 0 , - 7 + 2 \sqrt { 6 } )\)
• B) \(x ^ { 2 } + \frac { ( y + 7 ) ^ { 2 } } { 25 } = 1\)
• vertices: \(( - 12,0 ) , ( - 2,0 )\)
• foci \(( - 7 - 2 \sqrt { 6 } , 0 ) , ( - 7 + 2 \sqrt { 6 } , 0 )\)
• C) \(x ^ { 2 } + \frac { ( y - 7 ) ^ { 2 } } { 25 } = 1\)
• vertices: \(( 2,0 ) , ( 12,0 )\)
• foci \(( 7 - 2 \sqrt { 6 } , 0 ) , ( 7 + 2 \sqrt { 6 } , 0 )\)
• D) \(x ^ { 2 } + \frac { ( y - 7 ) ^ { 2 } } { 25 } = 1\)
• vertices: \(( 0,2 ) , ( 0,12 )\)
• foci \(( 0,7 - 2 \sqrt { 6 } ) , ( 0,7 + 2 \sqrt { 6 } )\)

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