Conic Sections in Polar Coordinates
1 Define Conics in Terms of a Focus and a Directrix
-$$r = \frac { 9 } { 3 - 3 \cos \theta }$$
A) parabola; The directrix is 3 unit(s) to the left of the pole at $x = - 3$.
B) parabola; The directrix is 3 unit(s) to the right of the pole at $x = 3$.
C) parabola; The directrix is 3 unit(s) above the pole at $y = 3$.
D) parabola; The directrix is 3 units below the pole at $\mathrm { y } = - 3$.

Question

Quizplus · Accepted Answer

The equation is in the form $r = \frac { ep } { 1 - e \cos \theta }$, which is the polar equation of a parabola with eccentricity $e = 1$. The directrix is $p$ units to the left of the pole if $p < 0$, and $p$ units to the right of the pole if $p > 0$. In this case, $p = -3$, so the directrix is 3 units to the left of the pole.

Conic Sections in Polar Coordinates 1 Define Conics in Terms r=93−3cos⁡θr = \frac { 9 } { 3 - 3 \cos \theta }r=3−3cosθ9​

Conic Sections in Polar Coordinates
1 Define Conics in Terms $r = \frac { 9 } { 3 - 3 \cos \theta }$