Find a polar equation of the conic with the given characteristics and with one focus at the pole. $\begin{array} { c c c } \text { Conic } & \text { Eccentricity } & \text { Directrix } \ \text { Hyperbola } & e = 5 & x = 2 \end{array}$
A) $r = \frac { 10 } { 1 - 5 \cos \theta }$
B) $r = \frac { 10 } { 1 + 5 \cos \theta }$
C) $r = \frac { 2 } { 1 + 5 \cos \theta }$
D) $r = \frac { 10 } { 1 + 5 \sin \theta }$
E) $r = \frac { 10 } { 1 - 5 \sin \theta }$

Question

Quizplus · Accepted Answer

Since the directrix is a vertical line, the focus is on the y-axis. Therefore, the polar equation of the hyperbola is of the form $r = \frac{ed}{1 - e \cos 	heta}$, where $e = 5$ is the eccentricity and $d$ is the distance from the pole to the directrix. Since the directrix is the line $x = 2$, we have $d = 2$. Substituting these values, we get $r = \frac{10}{1 + 5\cos 	heta}$. Therefore, the answer is choice B.

Find a Polar Equation of the Conic with the Given Conic Eccentricity Directrix Hyperbola e=5x=2\begin{array} { c c c } \text { Conic } & \text { Eccentricity } & \text { Directrix } \\ \text { Hyperbola } & e = 5 & x = 2 \end{array} Conic Hyperbola ​ Eccentricity e=5​ Directrix x=2​

Find a Polar Equation of the Conic with the Given $\begin{array} { c c c } \text { Conic } & \text { Eccentricity } & \text { Directrix } \\ \text { Hyperbola } & e = 5 & x = 2 \end{array}$