Find the eccentricity of the polar equation $$r = - \frac { 40 } { 20 + 41 \sin \theta }$$
A) $\frac { 41 } { 40 }$
B) $\frac { 20 } { 41 }$
C) $\frac { 1 } { 41 }$
D) $\frac { 1 } { 20 }$
E) $\frac { 41 } { 20 }$

Question

Find the eccentricity of the polar equation $$r = - \frac { 40 } { 20 + 41 \sin \theta }$$ 
A) $\frac { 41 } { 40 }$
B) $\frac { 20 } { 41 }$
C) $\frac { 1 } { 41 }$
D) $\frac { 1 } { 20 }$
E) $\frac { 41 } { 20 }$

Quizplus · Accepted Answer

The given polar equation is in the form $ r = \frac{ed}{1 + e \sin \theta} $, where $ e $ is the eccentricity. Comparing with $ r = - \frac{40}{20 + 41 \sin \theta} $, we have $ ed = 40 $ and $ e = \frac{41}{20} $.

Find the Eccentricity of the Polar Equation r=−4020+41sin⁡θr = - \frac { 40 } { 20 + 41 \sin \theta }r=−20+41sinθ40​

Find the Eccentricity of the Polar Equation $r = - \frac { 40 } { 20 + 41 \sin \theta }$