All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Angle of view - Ellipse and Hyperbola (Posted on 2011-11-24)
Given the equation x2/9 + y2/4 = 1 find the set of all points from which the angle of view* of this ellipse is a right angle. What is the significance of this set of points?

Given the equation x2/9 - y2/4 = 1 find the set of all points from which the angle of view* of this hyperbola is a right angle. What is the significance of this set of points?

* i.e. displaying a right angle between the two tangents.

 No Solution Yet Submitted by Jer Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(4): An asymptotic view (spoiler) Comment 7 of 7 |
(In reply to re(3): An asymptotic view (spoiler) by Bractals)

Yes, I see what you mean Bractals, but I'm not claiming that this parallel line is a tangent to the hyperbola. I quite agree that from that point P there isn't a tangent to that 'edge' of the hyperbola.
However, for a=b, if you take the line through P parallel to theta=45 and reduce its gradient by any amount it will cross the hyperbola and can't therefore be a limiting ray for the viewing angle. So that parallel line would be seen by an observer at P as the limiting ray (assuming they could see to infinity).

Edited on November 27, 2011, 3:30 pm
 Posted by Harry on 2011-11-27 15:29:45

Please log in:
 Login: Password: Remember me: Sign up! | Forgot password

 Search: Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information