Find the Eccentricity and Distance from the Pole to the Directrix

question 19

Multiple Choice

Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results. $r = \frac { 2 } { 7 + 5 \sin \theta }$

• A) eccentricity: \(\frac { 7 } { 5 }\) distance from pole to directrix: \(\frac { 5 } { 7 } \quad\) The graph is an ellipse.
• B) eccentricity: \(\frac { 5 } { 7 }\) distance from pole to directrix: \(\frac { 7 } { 5 } \quad\) The graph is a hyperbola.
• C) eccentricity: \(\frac { 7 } { 5 }\) distance from pole to directrix: \(\frac { 5 } { 7 }\) The graph is a hyperbola.
• D) eccentricity: \(\frac { 5 } { 7 }\) distance from pole to directrix: \(\frac { 7 } { 5 }\) \(\quad\) The graph is an ellipse.
• E) eccentricity: \(\frac { 7 } { 5 }\) distance from pole to directrix: \(\frac { 7 } { 5 }\) \(\quad\) The graph is an ellipse.

---

Definitions:

Associations

Connections or links between thoughts, ideas, or memories that can influence an individual's emotional responses and behavior.

Node

A basic unit or point in a network or system where connections are made.

Anterograde Amnesia

A condition where an individual is unable to form new memories after the onset of amnesia.

Brain Tumor

An abnormal growth of cells within the brain that can be benign or malignant, affecting various brain functions.