> cos(s) = cos(p) ecc where ecc is a constant. > > Use differential relations between r,th (polar) and > d x,y (cartesian) coordinates with respect to arc > length s. > > dr/ds - dx/ds ecc = 0 which integrates to > > r - x ecc = r - r cos(th) ecc = p, an arbitrary > y constant. > > 1 - ecc cos(th) = p/r the polar equation of all > l conics. > > Given constant is eccentricity and arbitray constant > t is semi-latus rectum. > > This rotational definition imho is much better than > n the standard distance definition of conics with > respect to the meaning and significance of > eccentricity.
Graphic showing equivalence of these two definitions is given: