Conic Sections in Polar Coordinates
1 Define Conics in Terms of a Focus and a Directrix
-$$r = \frac { 4 } { 2 + 2 \sin \theta }$$
A) parabola; The directrix is 2 unit(s) above the pole at $y = 2$.
B) parabola; The directrix is 2 unit(s) to the right of the pole at $x = 2$.
C) hyperbola; The directrix is 2 unit(s) above the pole at $y = 2$.
D) hyperbola; The directrix is 2 unit(s) to the right of the pole at $x = 2$.

Question

Quizplus · Accepted Answer

The given equation is in the form $r = \frac{e \cdot d}{1 + e \cos \theta}$ or $r = \frac{e \cdot d}{1 + e \sin \theta}$, where $e$ is the eccentricity and $d$ is the perpendicular distance from the directrix to the focus. For a parabola, $e = 1$. The equation $r = \frac{4}{2 + 2\sin \theta}$ simplifies to $r = \frac{2}{1 + \sin \theta}$, indicating a parabola with a directrix 2 units above the pole at $y = 2$, since the $\sin \theta$ term suggests vertical orientation.

Conic Sections in Polar Coordinates 1 Define Conics in Terms r=42+2sin⁡θr = \frac { 4 } { 2 + 2 \sin \theta }r=2+2sinθ4​

Conic Sections in Polar Coordinates
1 Define Conics in Terms $r = \frac { 4 } { 2 + 2 \sin \theta }$