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
> Your asymptotes will pass through the center and the points where the arc
> crosses the perpendicular line.
> Jim Osborn