If the Equation Represents a Hyperbola, Find the Center, Foci $$6 x ^ { 2 } - y ^ { 2 } - 72 x + 12 y - 114 = 0$$

question 78

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.
- $$6 x ^ { 2 } - y ^ { 2 } - 72 x + 12 y - 114 = 0$$

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

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Definitions:

Pluripotent

The ability of a stem cell to differentiate into any type of cell in the body but not capable of forming an entire organism.

Totipotent

Cells that have the potential to differentiate into any type of cell in an organism, including the placental cells.

Differentiated

A state in which cells have developed specialized functions and characteristics, differing from their originating stem cells.

Amnion

A thin, protective membrane that surrounds the embryo or fetus in the amniotic sac, containing the amniotic fluid.