How do you find the eccentricity, directrix, focus and classify the conic section $r = \frac{2}{1 + 2 cos θ}$ $r=2/(1+2costheta)$ ?

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How do you find the eccentricity, directrix, focus and classify the conic section $r = \frac{2}{1 + 2 cos θ}$ $r=2/(1+2costheta)$ ?

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Answer 1 · 2018-06-16T12:58:49

Eccentricity is $2$ $2$ , Focus is at the pole $(0, \frac{π}{2})$ $(0,pi/2)$ ,
Directrix is $p = 1$ $p=1$ unit at right from the pole.
Conic: Hyperbola

Explanation:

$r = \frac{2}{1 + 2 cos θ}$ $r= 2/(1+2 cos theta$ .The equation is in the form

$r = \frac{e p}{1 + e cos θ}; e = 2$ $r= (ep) /(1+e cos theta) ; e =2$ since $e > 1$ $e >1$ the conic

is hyperbola. $r= (ep) /(1+e cos theta) ; e p =2 :. p=1$

Directrix is at $p=1$ unit at right from the pole.

Eccentricity is $2$ , Focus is at the pole $(0,pi/2)$ [Ans]

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How do you find the eccentricity, directrix, focus and classify the conic section $r = \frac{2}{1 + 2 cos θ}$ $r=2/(1+2costheta)$ ?

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Explanation:

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How do you find the eccentricity, directrix, focus and classify the conic section r=2/(1+2costheta)r=21+2cosθr=2/(1+2costheta)?

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How do you find the eccentricity, directrix, focus and classify the conic section $r = \frac{2}{1 + 2 cos θ}$ $r=2/(1+2costheta)$ ?