Write a polar equation of the conic that has a focus at the origin, eccentricity , and directrix . Identify the conic.
A) , ellipse
B) , ellipse
C) , hyperbola
D) , hyperbola

Question

Write a polar equation of the conic that has a focus at the origin, eccentricity  , and directrix  . Identify the conic.
A) , ellipse 
B) , ellipse 
C) , hyperbola 
D) , hyperbola

Quizplus · Accepted Answer

A polar equation for a hyperbola with focus at the origin and directrix in polar form is given by $r=\frac{ed}{1+e\cos{	heta}}$, where $e$ is the eccentricity, $d$ is the distance from the origin to the directrix, and $	heta$ is the polar angle. Plugging in the given values, we get $r=\frac{11}{1+11\cos{	heta}}$. This is the equation of a hyperbola. Therefore, the answer is C.

Write a Polar Equation of the Conic That Has a Focus