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. $r = \frac { 2 } { 3 + \cos \theta }$
A) eccentricity: $\frac { 1 } { 3 }$ distance from pole to directrix: 2 The graph is an ellipse.
B) eccentricity: 3 distance from pole to directrix: $\frac { 1 } { 2 } \quad$ The graph is an ellipse.
C) eccentricity: $\frac { 1 } { 3 }$ distance from pole to directrix: $\frac { 1 } { 2 }$ The graph is an ellipse.
D) eccentricity: 3 distance from pole to directrix: 2 The graph is a hyperbola.
E) eccentricity: 3 distance from pole to directrix: $\frac { 1 } { 2 }$ The graph is a hyperbola.

Question

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. $r = \frac { 2 } { 3 + \cos \theta }$
A) eccentricity: $\frac { 1 } { 3 }$ distance from pole to directrix: 2 The graph is an ellipse. 
B) eccentricity: 3 distance from pole to directrix: $\frac { 1 } { 2 } \quad$ The graph is an ellipse. 
C) eccentricity: $\frac { 1 } { 3 }$ distance from pole to directrix: $\frac { 1 } { 2 }$ The graph is an ellipse. 
D) eccentricity: 3 distance from pole to directrix: 2 The graph is a hyperbola. 
E) eccentricity: 3 distance from pole to directrix: $\frac { 1 } { 2 }$ The graph is a hyperbola.

Quizplus · Accepted Answer

The Answer of 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. $r = \frac { 2 } { 3 + \cos \theta }$
A) eccentricity: $\frac { 1 } { 3 }$ distance from pole to directrix: 2 The graph is an ellipse. 
B) eccentricity: 3 distance from pole to directrix: $\frac { 1 } { 2 } \quad$ The graph is an ellipse. 
C) eccentricity: $\frac { 1 } { 3 }$ distance from pole to directrix: $\frac { 1 } { 2 }$ The graph is an ellipse. 
D) eccentricity: 3 distance from pole to directrix: 2 The graph is a hyperbola. 
E) eccentricity: 3 distance from pole to directrix: $\frac { 1 } { 2 }$ The graph is a hyperbola.

Find the Eccentricity and Distance from the Pole to the Directrix