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

Question

Quizplus · Accepted Answer

The equation is in the form $r = \frac {ep}{1 - e\sin \theta}$, where $e$ is the eccentricity and $p$ is the distance from the pole to the directrix. In this case, $e = 3$ and $p = 1$, so the conic is a hyperbola. The directrix is 1 unit below the pole because the sine of an angle is negative when the angle is in the third or fourth quadrant.

Conic Sections in Polar Coordinates 1 Define Conics in Terms r=31−3sin⁡θ\mathrm { r } = \frac { 3 } { 1 - 3 \sin \theta }r=1−3sinθ3​

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