Steven
Posts:
4
Registered:
6/30/12


How to find the major and minor axes of an ellipse with known centre and a single point?
Posted:
Oct 23, 2012 5:28 AM


Given : the centre (xc, yc), a point on the ellipse (x, y) the ratio of the length of the major (a) to minor (b) semiaxes (r = b/a) and the angle of rotation of the major semiaxis from the positive xaxis (t)
then, the following expression evaluates to 1 for for a point lying on the ellipse with major axis length, a:
[(xxc) * cos(t)  (yyc) * sin*(t)]^2/a^2 + [(xxc) * cos(t)  (yyc) * sin*(t)]^2/(a/r)^2
(see other threads by Roger Stafford)
If we let P = [(xxc) * cos(t)  (yyc) * sin*(t)] then this simplifies (in appearance) to: P^2 / a^2 + P^2 / (a/r)^2 = 1
My question is, how can I solve this equation to find a?
(Please feel free to point out any other mistakes!!)
Best wishes Steven

