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Topic: Inverse of a conic with regard to the centre
Replies: 1   Last Post: Jul 28, 2011 7:38 AM

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Vivian DeRoth

Posts: 5
Registered: 7/27/11
Inverse of a conic with regard to the centre
Posted: Jul 27, 2011 7:57 PM
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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



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