Find a Rectangular Equation for the Plane Curve Defined by the Parametric

question 76

Multiple Choice

Find a rectangular equation for the plane curve defined by the parametric equations.
- $$x = 5 \cos t , y = - 2 \sin t ; 0 \leq t \leq 2 \pi$$

• A) \(4 x ^ { 2 } + 25 y ^ { 2 } = 100 ; - 5 \leq x \leq 5\)
• B) \(4 x ^ { 2 } - 25 y ^ { 2 } = 100 ; x \geq 5\)
• C) \(4 x ^ { 2 } + 25 y ^ { 2 } = 1 ; - \frac { 1 } { 5 } \leq x \leq \frac { 1 } { 5 }\)
• D) \(4 x ^ { 2 } - 25 y ^ { 2 } = 1 ; x \geq \frac { 1 } { 2 }\)

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Definitions:

Hippocampus

A region of the brain involved in the formation of new memories and associated with learning and emotions.

Amygdala

A region of the brain within the temporal lobe, crucial for emotion processing, memory, and decision-making.

Basal Ganglia

A group of structures in the brain involved in coordinating movement, as well as aspects of learning and emotional response.

Hindbrain

The posterior part of the brain that includes the cerebellum and brainstem, involved in regulating basic bodily functions.