Provide an Appropriate Response $r = \frac { 1 - a \cos \theta } { 1 + a \cos \theta }$

question 298

Essay

Provide an appropriate response.
-Consider the curves corresponding to polar equations of the form $r = \frac { 1 - a \cos \theta } { 1 + a \cos \theta }$ where $a > 0$ . Explain how the graph changes as a changes. Identify any values of a for which the basic shape of the curve changes.

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Definitions:

Union Forces

The armed forces of the United States (the North) during the American Civil War.

1863

The year 1863 is notable for several historical events, including the Emancipation Proclamation in the United States, which declared the freedom of slaves in Confederate-held territory during the American Civil War.

Northern Soldiers

Refers to the soldiers from the Union states who fought in the American Civil War against the Confederate states of the South.

Slavery

A system in which individuals are owned by others, deprived of personal freedom, and forced to perform labor or services.