Find the eccentricity of the conic.
$$r = \frac { 5 } { 8 - 5 \sin \theta }$$
A) $e = \frac { 8 } { 5 }$
B) $e = 8$
C) $e = \frac { 5 } { 8 }$
D) $e = - 5$
E) $e = 5$

Question

Quizplus · Accepted Answer

The eccentricity of a conic is given by $e = \sqrt { 1 - \frac { b^2 } { a^2 } } $. In this case, $a = 8$ and $b = 5$, so $e = \sqrt { 1 - \frac { 5^2 } { 8^2 } } = \sqrt { 1 - \frac { 25 } { 64 } } = \sqrt { \frac { 39 } { 64 } } = \frac { \sqrt { 39 } } { 8 } \approx 0.625$.

Find the Eccentricity of the Conic r=58−5sin⁡θr = \frac { 5 } { 8 - 5 \sin \theta }r=8−5sinθ5​

Find the Eccentricity of the Conic $r = \frac { 5 } { 8 - 5 \sin \theta }$