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.)
Hints/Tips Solution - Proof upon request. | Comment 1 of 7

For the curve
    x^2         y^2
   ----- + s * ----- = 1,
    a^2         b^2
the circle
   x^2 + y^2 = a^2 + s * b^2
is the locus of points with
an angle of view of 90 degrees.
Where s = +1 for an ellipse and
      s = -1 for a hyperbola.
This was discovered with a 
combination of algebra and
Geometer's Sketchpad.
Note: The four points (a,b), (-a,b), 
      (-a,-b), and (a,-b) are
      clearly members of the locus
      for the ellipse.
Note: For the hyperbola - if b >= a,
      then there are no points with
      an angle of view of 90 degrees.
 

  Posted by Bractals on 2011-11-24 14:28:58
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