Select the Answer That Represents the Hyperbola as Well as Its

question 4

Multiple Choice

Select the answer that represents the hyperbola as well as its eccentricity, center and values of $a$ , $b$ and $c$ . $r = \frac { 5 } { 2 + 6 \cos \theta }$

• A) Eccentricity: \(3\) Center: \(\left( \frac { 15 } { 16 } , 0 \right)\) \(a = \frac { 5 } { 16 } , b = \frac { 5 \sqrt { 2 } } { 8 } , c = \frac { 15 } { 16 }\)
• B) Eccentricity: \(3\) Center: \(\left( - \frac { 15 } { 16 } , 0 \right)\) \(a = \frac { 5 } { 16 } , b = \frac { 5 \sqrt { 2 } } { 8 } , c = \frac { 15 } { 16 }\)
• C) Eccentricity: \(3\) Center: \(\left( \frac { 1 } { 2 } , 0 \right)\) \(a = \frac { 1 } { 6 } , b = \frac { \sqrt { 2 } } { 3 } , c = \frac { 1 } { 2 }\)
• D) Eccentricity: \(3\) Center: \(\left( - \frac { 1 } { 2 } , 0 \right)\) \(a = \frac { 1 } { 6 } , b = \frac { \sqrt { 2 } } { 3 } , c = \frac { 1 } { 2 }\)
• E) Eccentricity: \(3\) Center: \(\left( \frac { 15 } { 16 } , 0 \right)\) \(a = \frac { 1 } { 6 } , b = \frac { \sqrt { 2 } } { 3 } , c = \frac { 1 } { 2 }\)

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Definitions:

Localization

The concept or process of identifying the specific location or area within a larger context, such as localizing a function within the brain.

Lateralization

The preference of certain brain functions or thought processes to be more prevalent in one brain hemisphere over the other.

Neurogenesis

Neurogenesis is the process of formation of new neurons in the brain, contributing to brain plasticity and regeneration.

Plasticity

the capacity of the brain to change and adapt in response to experience, injury, or environment, including the formation of new neural connections.