Find a polar equation for the conic. A focus is at the pole.
-$\mathrm { e } = 1$; directrix is parallel to the polar axis 1 above the pole
A) $r = \frac { 3 } { 1 + \cos \theta }$
B) $r = \frac { 3 } { 1 + \sin \theta }$
C) $r = \frac { 3 } { 1 - \cos \theta }$
D) $r = \frac { 3 } { 1 - \sin \theta }$

Question

Quizplus · Accepted Answer

The given conditions describe a conic with eccentricity $e = 1$, indicating a parabola. Since the directrix is parallel to the polar axis and above the pole, the parabola opens downwards. The correct polar equation for such a parabola is $r = \frac { 3 } { 1 + \sin \theta }$, which matches choice B. This equation accounts for the orientation and position of the parabola relative to the pole and the directrix.

Find a Polar Equation for the Conic e=1\mathrm { e } = 1e=1

Find a Polar Equation for the Conic $\mathrm { e } = 1$