How do you identify the conic of # r = 2/(1 + 2 cosx)#?
it represents the equation of a hyperbola
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
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
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..