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Topic: Same intersection angles in ellipse
Replies: 6   Last Post: Oct 29, 2013 3:11 PM

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Peter Scales

Posts: 192
From: Australia
Registered: 4/3/05
Re: Same intersection angles in ellipse
Posted: Oct 20, 2013 2:02 PM
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> Sum of of two focal rays lengths (from one focus) of
> an ellipse (semi major, minor axes a,b) is given as
> 2a. Show they make equal angles to the ellipse.. and
> find it.


If I haven't misunderstood the question the two focal rays from F1 meet the ellipse at diametrically opposite points P1 and P2, from the definition of an ellipse.

The tangents at P1 and P2 are parallel, and bisect the external angle between the focal rays. The figure has rotational symmetry at Pi radians, so the angles at P1(x1,y1) and P2(-x1,-y1) are equal to theta, where

tan(theta) = b^2/(c.y1)

Regards, Peter Scales.

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