Identify the conic that the polar equation represents. Also, give the position of the directrix.
-$$r = \frac { 5 } { 6 - 3 \sin \theta }$$
A) ellipse, directrix perpendicular to the polar axis $\frac { 5 } { 3 }$ right of the pole
B) ellipse, directrix parallel to the polar axis $\frac { 5 } { 3 }$ above the pole
C) ellipse, directrix parallel to the polar axis $\frac { 5 } { 3 }$ below the pole
D) ellipse, directrix perpendicular to the polar axis $\frac { 5 } { 3 }$ left of the pole

Question

Quizplus · Accepted Answer

The given polar equation is of the form $ r = \frac{ed}{1 - e \sin \theta} $, where $ e = \frac{3}{6} = \frac{1}{2} $, indicating an ellipse. The directrix is parallel to the polar axis and located $\frac{5}{3}$ below the pole.

Identify the Conic That the Polar Equation Represents r=56−3sin⁡θr = \frac { 5 } { 6 - 3 \sin \theta }r=6−3sinθ5​

Identify the Conic That the Polar Equation Represents $r = \frac { 5 } { 6 - 3 \sin \theta }$