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Re: Locus for ratio of cosine of angles to be constant
Posted:
Nov 18, 2013 7:18 AM


> 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 semilatus 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:
http://i43.tinypic.com/2med8x4.jpg
It considers the right angle subtended by tangent point to directrix line segment at focus.
Regards Narasimham



