Date: Feb 21, 1995 10:09 AM
Author: Jim Osborn
Subject: Re: Hyperbola

> On Mon, 20 Feb 1995, Diana M Thompson wrote:

>

> > I was delighted to work out how to find the focus of the parabola by

> > construction, but am a little stumped by how to find the asymptotes of the

> > hyperbola (without advance knowledge of the equation, and other than simply

> > "eyeballing" the asymptote).

> >

> > Is it possible? Or does someone out there have a better way?

> >

> > D. Thompson

> > Montebello Unified School District

> > Montebello, CA

>

> After you find the focii of the hyperbola draw a line connecting them and

> find the center (the center of the hyperbola). Find the distance from

> the center to one of the focii call it c. Find the distance from the

> center to one of the vertices call it a. Find the distance b using

> c^2 = a^2 + b^2 or you can have them find the second side of a right

> triangle with hypotenuse c and side a. Construct b perpendicular to the

> line connecting the focii at one of the vertices. Your asymptote will through

> the center of the hyperbola and the end of line segment b. Construct the

> line in the opposite direction to get your other asymptote.

>

>

> To construct this swing an arc from the center of the hyperbola with its

> radius equal to the distance from the center to one of the focii.

> Construct a line perpendicular to the line connecting the focii at one of the

> vertices.

> Your asymptotes will pass through the center and the points where the arc

> crosses the perpendicular line.

>

> Jim Osborn

> josborn@genesee.freenet.org