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Topic: Inverse of a conic with regard to the centre is an oval of Cassini
Replies: 6   Last Post: Jul 28, 2011 7:33 AM

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Rob Johnson

Posts: 1,771
Registered: 12/6/04
Re: Inverse of a conic with regard to the centre is an oval of Cassini
Posted: Jul 28, 2011 1:33 AM
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In article <>,
Ken Pledger <> wrote:
>In article <>, Rob Johnson <>

>> ....
>> If we invert the points (x -> x/r^2, y -> y/r^2) ....

>x -> (r^2)/x, y -> (r^2)/y ?

The direction is preserved, but the distance is inverted. That
means x -> x/r^2 and y -> y/r^2. This is made explicit in


I have used a radius of 1 since inversions with different radii are
simply dilations of each other.

You can also check Section 2 of


Rob Johnson <>
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