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Topic: How to find the major and minor axes of an ellipse with known centre and a single point?
Replies: 3   Last Post: Oct 23, 2012 2:59 PM

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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
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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 x-axis (t)

then, the following expression evaluates to 1 for for a point lying on the ellipse with major axis length, a:

[(x-xc) * cos(t) - (y-yc) * sin*(t)]^2/a^2 + [(x-xc) * cos(t) - (y-yc) * sin*(t)]^2/(a/r)^2

(see other threads by Roger Stafford)

If we let P = [(x-xc) * cos(t) - (y-yc) * 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



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