Find the Eccentricity and Distance from the Pole to the Directrix

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.