Select the Answer That Represents the Hyperbola as Well as Its

Multiple Choice

Select the answer that represents the hyperbola as well as its eccentricity, center and values of $a$ , $b$ and $c$ . $r = \frac { 5 } { 2 + 6 \cos \theta }$

A) Eccentricity: $3$ Center: $\left( \frac { 15 } { 16 } , 0 \right)$ $a = \frac { 5 } { 16 } , b = \frac { 5 \sqrt { 2 } } { 8 } , c = \frac { 15 } { 16 }$
B) Eccentricity: $3$ Center: $\left( - \frac { 15 } { 16 } , 0 \right)$ $a = \frac { 5 } { 16 } , b = \frac { 5 \sqrt { 2 } } { 8 } , c = \frac { 15 } { 16 }$
C) Eccentricity: $3$ Center: $\left( \frac { 1 } { 2 } , 0 \right)$ $a = \frac { 1 } { 6 } , b = \frac { \sqrt { 2 } } { 3 } , c = \frac { 1 } { 2 }$
D) Eccentricity: $3$ Center: $\left( - \frac { 1 } { 2 } , 0 \right)$ $a = \frac { 1 } { 6 } , b = \frac { \sqrt { 2 } } { 3 } , c = \frac { 1 } { 2 }$
E) Eccentricity: $3$ Center: $\left( \frac { 15 } { 16 } , 0 \right)$ $a = \frac { 1 } { 6 } , b = \frac { \sqrt { 2 } } { 3 } , c = \frac { 1 } { 2 }$