How do you name the curve given by the conic #r=6/(2+sintheta)#?
The polar equation of a conic, referred to a/the focus as the pole r =
0 and the perpendicular from the pole to the (corresponding)
directrix as the initial line
e is the eccentricity of the conic and l is the semi latus rectum = #
(1/2) X (length of the chord of the conic through the focus,that is
perpendicular to the initial line).
The conic is named an ellipse, parabola or hyperbola according as #
e < = > 1.#
Interestingly, for the circle the focus is at the center and l
= radius a and e = 0. The equation is simply r = a.
Here, the equation is
ellipse. The semi major axis a is given by