If the Equation Represents a Hyperbola, Find the Center, Foci $y ^ { 2 } - x ^ { 2 } - 14 y + 12 x - 36 = 0$

question 241

Multiple Choice

If the equation represents a hyperbola, find the center, foci, and asymptotes. If the equation represents an ellipse, find the center, vertices, and foci. If the equation represents a circle, find the center and radius. If the equation represents a parabola, find the focus and directrix.
- $y ^ { 2 } - x ^ { 2 } - 14 y + 12 x - 36 = 0$

• A) C: (6, 7); F: \(( 0,7 + 7 \sqrt { 2 } ) , ( 0,7 - 7 \sqrt { 2 } ) ; A : y - 7 = x - 6 , y - 7 = - ( x - 6 )\)
• B) C: \(( 6,0 ) ; F : ( 7 \sqrt { 2 } , 0 ) , ( - 7 \sqrt { 2 } , 0 ) ; A : y = \frac { 1 } { 7 } x , y = - \frac { 1 } { 7 } x\)
• C) C: \(( 6,7 ) ; F : ( 6,7 + 7 \sqrt { 2 } ) , ( 6,7 - 7 \sqrt { 2 } ) ; A : y - 7 = x - 6 , y - 7 = - ( x - 6 )\)
• D) C: \(( - 1,7 ) ; F : ( 7 \sqrt { 2 } , 0 ) , ( - 7 \sqrt { 2 } , 0 ) ; A : y = x , y = - x\)

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