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

question 99

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

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Definitions:

BASIC I.D.

An acronym in psychology that stands for Behavior, Affect, Sensation, Imagery, Cognition, Interpersonal relationships, and Drugs/biology, used to assess or plan treatment across multiple dimensions of a person's experience.

Affect

A term used in psychology to describe the experience of feeling or emotion.

Cognitions

Mental actions or processes of acquiring knowledge and understanding through thought, experience, and the senses.

Unified Protocol

A transdiagnostic cognitive-behavioral therapy approach designed to address a range of emotional disorders by targeting common underlying factors.