Find the eccentricity and identify the conic given by $r= 7 / ( 1 + 3 \sin \theta )$
A) $e = 3$
, hyperbola
B) $e = \frac { 3 } { 7 }$
, ellipse
C) $e = \frac { 7 } { 3 }$
, hyperbola
D) $e = 7$
, hyperbola
E) none of these

Question

Quizplus · Accepted Answer

The given equation is in the form $ r = \frac{ed}{1 + e \sin \theta} $, where $ e $ is the eccentricity. Comparing, $ e = 3 $. Since $ e > 1 $, the conic is a hyperbola.

Find the Eccentricity and Identify the Conic Given By r=7/(1+3sin⁡θ)r= 7 / ( 1 + 3 \sin \theta )r=7/(1+3sinθ)

Find the Eccentricity and Identify the Conic Given By $r= 7 / ( 1 + 3 \sin \theta )$