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I feel like this problem given to me is much easier than I'm making it out to be.

Basically I'm only asked to write the equation of a circle with a given centre $(a,b)$, then the projective equation of the circle with the same centre. How can I do this?

user577215664
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twistedshell
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1 Answers1

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Ordinary (affine) equation: $(x-a)^2+(y-b)^2=r^2$.

Substitute formally $x/z$ and $y/z$ instead of $x$ and $y$ and you will get the projective equation:

$$(x/z-a)^2+(y/z-b)^2=r^2$$

or (after formally multiplying by $z^2$):

$$(x-az)^2+(y-bz)^2=r^2z^2$$