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Inverse of a conic with regard to the centre
Posted:
Jul 27, 2011 7:57 PM


I came across the following link: http://www.archive.org/stream/differentialcalc00edwauoft/differentialcalc00edwauoft_djvu.txt which included the following few lines:  48. Show that the inverse of a conic with regard to the focus is a Lima^on (Equation r = a + b cos 0), which becomes a cardi oide if the conic be a parabola.
49. Show that the inverse of a conic with regard to the centre is an oval of Cassini (Equation r 2 = + 6cos2#), which becomes a Lemniscate of Bernoulli if the conic be a rectangular hyperbola.  I thought i read somewhere that the inverse of a Cassinian was a Cassinian  i think the word for this property is anagammatic or something like that.
Is that true what is said in 49. ie that the 'inverse of a conic with regard to the centre is an oval of Cassini'. If so can anyone point me towards sources that would show how this is.
Viv



