Conic Sections in Polar Coordinates
1 Define Conics in Terms of a Focus and a Directrix
-$$r = \frac { 6 } { 1 - 2 \cos \theta }$$
A) hyperbola; The directrix is 3 unit(s) to the left of the pole at $x = - 3$.
B) hyperbola; The directrix is 3 unit(s) to the right of the pole at $x = 3$.
C) ellipse; The directrix is 3 unit(s) to the left of the pole at $x = - 3$.
D) ellipse; The directrix is 3 unit(s) to the right of the pole at $x = 3$.

Question

Quizplus · Accepted Answer

The equation is in the form $r = \frac { ep } { 1 - e \cos \theta }$, which is the polar equation of a conic with eccentricity $e$ and directrix at $x = p$. In this case, $e = 2$ and $p = 3$, so the conic is a hyperbola with directrix at $x = 3$.

Conic Sections in Polar Coordinates 1 Define Conics in Terms r=61−2cos⁡θr = \frac { 6 } { 1 - 2 \cos \theta }r=1−2cosθ6​

Conic Sections in Polar Coordinates
1 Define Conics in Terms $r = \frac { 6 } { 1 - 2 \cos \theta }$