The Eccentricity Is Given of a Conic Section with One $r = \frac { 16 } { 1 - 2 \cos \theta }$

question 150

Multiple Choice

The eccentricity is given of a conic section with one focus at the origin, along with the directrix corresponding to that focus. Find a polar equation for the conic section.
-e = 2, x = -8

• A) \(r = \frac { 16 } { 1 - 2 \cos \theta }\)
• B) \(r = \frac { 16 } { 1 + 2 \cos \theta }\)
• C) \(r = \frac { 16 } { 1 + 8 \cos \theta }\)
• D) \(r = \frac { 16 } { 1 - 2 \sin \theta }\)

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Definitions:

Limbic System

A complex system of nerves and networks in the brain, associated with instincts, moods, and emotions.

Anterior Thalamus

A part of the thalamus located towards the front of the brain, playing a role in relaying sensory information and in the regulation of consciousness and sleep.

Medial Forebrain Bundle

A neural pathway in the brain that connects the brainstem to various structures in the forebrain, involved in the mediation of reward and pleasure.

Hippocampus

A curved structure located within the brain's temporal lobe, playing a central role in memory formation and spatial navigation.