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Re: Hyperbola
Posted:
Feb 21, 1995 10:09 AM


> 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



