How do you name the curve given by the conic $r=4/(1+2sintheta)$ ?

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Answer 1 · 2016-08-13T11:52:37

Hyperbola.

The polar equation $r = l/(1+e cos theta)$ represents a conic whose

eccentricity is e. A focus is the pole and the line from the pole away

from the center is the initial line $theta=0$ .

As $cos theta = sin (pi/2-theta)$ ,

transforming $(pi/2-theta) to theta$ ,

we get the equation in the given form

This transformation is rotation of the initial line through

$pi/2$ , about the pole, in the clockwise sense.

For e > 1, the conic is named a hyperbola..

Here $e = 2 and$

$l = 4= a(e^2-1)=3a$ , and so,

the semi major axis the hyperbola $a = 4/3.$ .

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How do you name the curve given by the conic r=4/(1+2sintheta)r=4/(1+2sintheta)?