
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 6th, 2012, 12:43 AM  #1 
Newbie Joined: Jan 2012 Posts: 29 Thanks: 0  Hyperbola and Line intersections
Consider the hyperbola x^2  y^2 = 1. A line in R^2 (All real numbers squared) can intersect this hyperbola in one of four ways: not at all, at one point crossing the hyperbola, at one point tangent to the hyperbola, and at two points. For each of the four cases, find a line which is an example of that case. I've never dealt with R^2 and I don't know how to solve this equation for any of the four intersections. I don't know where to begin on this one. 
February 6th, 2012, 02:32 AM  #2 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Hyperbola and Line intersections [color=#000000]Yellow line : y=x3 intersection at one point Blue line: x=1 tangent at one point Green line: y=3/2 intersection at two points Red line: x=1/2 intersection at zero points [attachment=0:m6hs8ojl]hyperbola.png[/attachment:m6hs8ojl] [/color] 
February 6th, 2012, 08:10 AM  #3 
Member Joined: Feb 2012 Posts: 36 Thanks: 0  Re: Hyperbola and Line intersections
The R^2 simply refers to two dimensional xy space. There are hyperboloids in 3 dimensional shape (for example electricity power station cooling towers) and indeed in more dimensions. These and the other conic sections are all examples of quadric surfaces. 

Tags 
hyperbola, intersections, line 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
intersections...  Prold  Real Analysis  2  April 21st, 2013 12:51 PM 
unions, intersections  annakar  Applied Math  5  January 11th, 2013 12:10 PM 
Find The Intersections Of A Circle and A Line  soulrain  Algebra  2  January 6th, 2012 10:21 AM 
points of intersections  functionman  Algebra  3  March 10th, 2011 08:46 AM 
Parabola and Line intersections?  organismal  Algebra  1  September 9th, 2009 09:06 PM 