My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum

LinkBack Thread Tools Display Modes
February 6th, 2012, 12:43 AM   #1
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.
Math4dummy is offline  
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=x-3 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

Attached Images
File Type: png hyperbola.png (22.7 KB, 87 views)
ZardoZ is offline  
February 6th, 2012, 08:10 AM   #3
Joined: Feb 2012

Posts: 36
Thanks: 0

Re: Hyperbola and Line intersections

The R^2 simply refers to two dimensional x-y 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.
dextrous is offline  

  My Math Forum > High School Math Forum > Algebra

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

Copyright © 2019 My Math Forum. All rights reserved.