Complete the Square to Determine the Type of Curve Represented $x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12$

question 16

Multiple Choice

Complete the square to determine the type of curve represented by the equation. $x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12$

• A) \(( x + 2 ) ^ { 2 } = 9 ( y - 3 )\) , parabola
• B) \(\frac { ( x + 2 ) ^ { 2 } } { 81 } + \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1\), ellipse
• C) \(\frac { ( x + 2 ) ^ { 2 } } { 8 } - \frac { ( y - 3 ) ^ { 2 } } { 4 } = 1\), hyperbola
• D) \(\frac { ( x + 3 ) ^ { 2 } } { 9 } - \frac { ( y - 2 ) ^ { 2 } } { 3 } = 1\), hyperbola
• E) none of these

---

Definitions:

Genetic Component

Refers to the contribution of genes or heredity to the development of traits, behaviors, or diseases.

Genetic Vulnerability

A predisposition to develop certain medical conditions or diseases based on an individual's genetic makeup.

Depressive Disorder

This condition involves a constant feeling of sadness or a disinterest in usual activities, markedly affecting a person's daily routine.

Neurochemical Bases

Refers to the foundational role that neurotransmitters and other chemicals play in the functioning of the nervous system and the brain.