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On the stationary eccentricity of a system of four-tangent conics

Published online by Cambridge University Press:  20 January 2009

F. E. Edwards
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Let the convex quadrilateral formed by the four given tangents be ABA′B′, and O the intersection of the diagonals. Let OA and OB be taken as axes of x and y. Denote OA, OA′, OB and OB′ by a, a′, b and b′, a and b being positive, and a′ and b′ negative. The tangential equation of the system is then

where k is a variable parameter; for the equation is satisfied when the straight line lx + my + 1 = 0 passes through any two adjacent angular points of the quadrilateral.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 28 , February 1909 , pp. 2 - 5
Copyright
Copyright © Edinburgh Mathematical Society 1909

References

page 3 note * The ellipses of the system are always real, for the equation referred to the centre as origin is . Hence the ellipses are real as long as B is negative. Now which is negative when k is within the elliptio limits.