Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Math Topics » geometry.puzzles.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Peter Scales

Posts: 163
From: Australia
Registered: 4/3/05
Re: Same intersection angles in ellipse
Posted: Oct 20, 2013 2:02 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

> 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.


Narasimham,

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.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.