VI.—Note on Confocal Conic Sections

H. F. Talbot
1865 Transactions of the Royal Society of Edinburgh  
A short paper of mine on Fagnani's theorem, and on Confocal Conic Sections, was inserted in the twenty-third volume of the Transactions of the Royal Society. Some of the conclusions of that paper can, however, be obtained more simply, as I will now proceed to show.I will, in the first place, resume the problem—"To find the intersection of a confocal ellipse and hyperbola."Since the curves have the same foci, and therefore the same centre, let the distance between the centre and focus be
more » ... nd focus be calledunity, since it is the same for both curves. Leta, b, be the axes of the ellipse, A, B, those of the hyperbola. Then we have 1 =a2−b2= A2+ B2, which equation expresses the condition of confocality.
doi:10.1017/s008045680003163x fatcat:6tlidzwjizbfnc5wwpwfgp5efe