Conic Sections in Polar Coordinates
1 Define Conics in Terms of a Focus and a Directrix
-$$r = \frac { 3 } { 6 - 3 \sin \theta }$$
A) ellipse; The directrix is 1 unit(s) below the pole at $y = - 1$.
B) ellipse; The directrix is 1 unit(s) to the left of the pole at $x = - 1$.
C) ellipse; The directrix is 1 unit(s) to the right of the pole at $x = 1$.
D) ellipse; The directrix is 1 unit(s) above the pole at $\mathrm { y } = 1$.

Question

Quizplus · Accepted Answer

The equation $$r = \frac { 3 } { 6 - 3 \sin \theta }$$ can be rewritten as $$r = \frac { e } { 1 - e \sin \theta }$$ where $e = \frac{1}{2}$, indicating an ellipse. The directrix is perpendicular to the axis of symmetry, which for $\sin \theta$ is vertical, and since the coefficient of $\sin \theta$ is negative, the directrix is below the pole, making the correct answer A.

Conic Sections in Polar Coordinates 1 Define Conics in Terms r=36−3sin⁡θr = \frac { 3 } { 6 - 3 \sin \theta }r=6−3sinθ3​

Conic Sections in Polar Coordinates
1 Define Conics in Terms $r = \frac { 3 } { 6 - 3 \sin \theta }$