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 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
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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

[attachment=0:m6hs8ojl]hyperbola.png[/attachment:m6hs8ojl]
[/color]
Attached Images hyperbola.png (22.7 KB, 87 views) 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 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. Tags hyperbola, intersections, line hyperbola intersections

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