The Eccentricity Is Given of a Conic Section with One $$e = \frac { 1 } { 3 } , y = 5$$

question 69

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.
- $$e = \frac { 1 } { 3 } , y = 5$$

• A) \(r = \frac { 5 } { 3 - \sin \theta }\)
• B) \(r = \frac { 5 } { 3 + \sin \theta }\)
• C) \(r = \frac { 5 } { 1 + 3 \cos \theta }\)
• D) \(r = \frac { 5 } { 3 + \cos \theta }\)

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Definitions:

Energy Minima

Points in a potential energy surface that represent stable states of a system, where any small displacement of particles leads to an increase in potential energy.

Dihedral Angle

The angle between two planes defined by four atoms, often used to describe the orientation of parts of a molecule relative to each other.

Steric Strain

A form of strain in molecules resulting from repulsive interactions when atoms are forced too close to one another, influencing molecule stability and reactivity.

Torsion Strain

Internal strain in a molecule caused by the electron cloud repulsions when bonds are twisted away from their preferred angles.