Find a polar equation for the conic. A focus is at the pole.
-$\mathrm { e } = 5$; directrix is perpendicular to the polar axis 3 to the right of the pole
A) $r = \frac { 15 } { 1 + 5 \cos \theta }$
B) $r = \frac { 15 } { 1 + 5 \sin \theta }$
C) $r = \frac { 15 } { 1 - 5 \sin \theta }$
D) $r = \frac { 15 } { 1 - 5 \cos \theta }$

Question

Quizplus · Accepted Answer

The polar equation for a conic with a focus at the pole is $r = \frac { ed } { 1 \pm e \cos \theta }$ or $r = \frac { ed } { 1 \pm e \sin \theta }$, where $e$ is the eccentricity and $d$ is the perpendicular distance from the directrix to the pole. Given $e = 5$ and the directrix is 3 units to the right of the pole, $d = 3$. Since the directrix is perpendicular to the polar axis and to the right, the equation uses $\cos \theta$, and because the directrix is to the right, we use $+$ in the denominator. Thus, $r = \frac { 15 } { 1 + 5 \cos \theta }$.

Find a Polar Equation for the Conic e=5\mathrm { e } = 5e=5

Find a Polar Equation for the Conic $\mathrm { e } = 5$