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 given equation is in the form of a conic section in polar coordinates, $r = \frac{l}{1 - e\sin\theta}$, where $e$ is the eccentricity. Comparing this with the given equation, $r = \frac{5}{8 - 5\sin\theta}$, we can rewrite the denominator as $1 - \frac{5}{8}\sin\theta$. This shows that $e = \frac{5}{8}$, which corresponds to choice C.

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 $r = \frac { 5 } { 8 - 5 \sin \theta }$