Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: Locus for ratio of cosine of angles to be constant
Posted:
Nov 17, 2013 10:44 AM


cos(s) = cos(p) ecc where ecc is a constant.
Use differential relations between r,th (polar) and 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 constant.
1  ecc cos(th) = p/r the polar equation of all conics.
Given constant is eccentricity and arbitray constant is semilatus rectum.
This rotational definition imho is much better than the standard distance definition of conics with respect to the meaning and significance of eccentricity.
Regards Narasimham



