# How do you identify the conic of # r = 2/(1 + 2 cosx)#?

##### 2 Answers

it represents the equation of a hyperbola

#### Explanation:

We know that the cartesian coordinate

The given equation

This is the cartesian form of the given polar equation.It is obvious from the equation that it represents the equation of a hyperbola.

Rearranging, the form is

#### Explanation:

The polar equation of a conic referred to a focus as pole and the

straight line from the pole to the center of the conic as the initial line

(

rectum.

This is derived using the property that

'the distance from the focus = eccentricity X distance from the

(corresponding ) directrix.

For a hyperbola, the eccentricity

Now, the given equation can be rearranged to this standard form

The semi transverse axis b = a sqrt(e^2-1)=(2/3)sqrt 3. > a..