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Conic-Tracing in Line Coordinates

Published online by Cambridge University Press:  03 November 2016

S. P. Johnson
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Extract

Consider x : y : 1 = t2 - 2t : t : t2 - t - 1. ........................ ( i)

The curve meets the line lx +my + n = 0 in points given by

l(t2 -2t) +mt +n(t2 -t-1) =0.

For any given Z, m, n there are two values of t. Hence the curve meets any line in two points and is therefore a conic. For a given l, m, n the values of t are the roots of the equation

t2 (l +n) + t(m -2l -n) -n =0.

Type
Research Article
Information
The Mathematical Gazette , Volume 19 , Issue 233 , May 1935 , pp. 94 - 97
Copyright
Copyright © Mathematical Association 1935

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