Identify the Conic by Writing the Equation in Standard Form $4 x ^ { 2 } + 4 y ^ { 2 } + 8 x - 16 y - 12 = 0$

question 36

Multiple Choice

Identify the conic by writing the equation in standard form.​ $4 x ^ { 2 } + 4 y ^ { 2 } + 8 x - 16 y - 12 = 0$ ​

• A) \(\frac { ( x + 1 ) ^ { 2 } } { \frac { 2 } { 4 } } + \frac { ( y - 2 ) ^ { 2 } } { \frac { 2 } { 4 } } = 8\) ;ellipse
• B) \(( x + 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 4\) ;circle
• C) \(( x + 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 8\) ;circle
• D) \(( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 8\) ;circle
• E) \(\frac { ( x + 1 ) ^ { 2 } } { \frac { 17 } { 4 } } + \frac { ( y - 2 ) ^ { 2 } } { \frac { 17 } { 4 } } = 8\) ;ellipse

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Definitions:

Lateral Hypothalamus

An area of the brain that regulates hunger and thirst.

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A region of the hypothalamus involved in regulating hunger and satiety signals, playing a critical role in energy homeostasis and weight regulation.

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The process that initiates, guides, and maintains goal-oriented behaviors.

Biological Need

A fundamental requirement that supports the survival and well-being of living organisms.