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

Home > Just Math
Angle of view - Ellipse and Hyperbola (Posted on 2011-11-24) Difficulty: 3 of 5
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.)
Some Thoughts re(3): An asymptotic view (spoiler) | Comment 6 of 7 |
(In reply to re(2): An asymptotic view (spoiler) by Harry)

For b = a and P in quadrant (45,135).

Let Q be the foot of the perpendicular from P to asymptote=45. If the ray from P is parallel to asymptote=45, then the distance from the ray to the branch of the hyperbola in quadrant (-45,45) is greater than |PQ|.

Seems a strange definition for a tangent line. But, it's a thoughtful point.

-------------------------------------------------------------------------

Bye the way, I liked your proof of the original problem. My proof started with a point on the curve and derived one of the other two points on the curve such that lines tangent to the curve at the starting point and the derived point are orthognal. Your proof took about a third of a page where mine took three to four pages.

Edited on November 27, 2011, 1:59 am
  Posted by Bractals on 2011-11-27 01:48:06

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 (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information