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: \(( 6,6 ) ; F : ( 6 + 7 \sqrt { 7 } , 6 ) , ( 6 - 7 \sqrt { 7 } , 6 ) ; A : y - 6 = \sqrt { 6 } ( x - 6 ) , y - 6 = - \sqrt { 6 } ( x - 6 )\)

---

Definitions:

Effect on Behavior

The impact that various factors, such as environment, psychology, and genetics, have on how individuals act or respond to situations.

Cocktail Party Phenomenon

The ability of individuals to focus their attention on a single conversation in a noisy environment, filtering out other conversations.

Phi Phenomenon

An optical illusion of perceived continuous motion between separate objects viewed rapidly in succession, such as in motion pictures.

Name-Orientation Response

The behavior in which an individual reacts to hearing their name, often used as an indicator of attention or awareness.