Write the Equation of the Hyperbola in Standard Form $$6 x ^ { 2 } - 5 y ^ { 2 } + 60 x - 20 y + 100 = 0$$

question 8

Multiple Choice

Write the equation of the hyperbola in standard form. Identify the center and foci.
- $$6 x ^ { 2 } - 5 y ^ { 2 } + 60 x - 20 y + 100 = 0$$

• A) \(\frac { ( x + 5 ) ^ { 2 } } { 5 } - \frac { ( y + 2 ) ^ { 2 } } { 6 } = 0\)
• center: \(( - 5 , - 2 )\)
• foci: \(( - 5 + \sqrt { 11 } , - 2 ) , ( - 5 - \sqrt { 11 } , - 2 )\)
• B) \(\frac { ( x - 5 ) ^ { 2 } } { 5 } - \frac { ( y - 2 ) ^ { 2 } } { 6 } = 1\)
• center: \(( 5,2 )\)
• foci: \(( 5 + \sqrt { 11 } , 2 ) , ( 5 - \sqrt { 11 } , 2 )\)
• C) \(\frac { ( x + 5 ) ^ { 2 } } { 5 } - \frac { ( y + 2 ) ^ { 2 } } { 6 } = 1\)
• center: \(( - 5 , - 2 )\)
• foci: \(( - 5 + \sqrt { 11 } , - 2 ) , ( - 5 - \sqrt { 11 } , - 2 )\)
• D) \(\frac { ( x - 5 ) ^ { 2 } } { 5 } - \frac { ( y - 2 ) ^ { 2 } } { 6 } = 0\)
• center: \(( 5,2 )\)
• foci: \(( 5 + \sqrt { 11 } , 2 ) , ( 5 - \sqrt { 11 } , 2 )\)

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