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November 13th, 2010, 12:36 PM   #1
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Circle Problem

Find a necessary and sufficient condition on A, B, C, D, and E for Ax^2 + By^2 + Cx + Dy + E = 0 to be an equation of a circle.
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November 13th, 2010, 03:57 PM   #2
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Re: Circle Problem

Hello, julian21!

I'll give this a try . . .


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November 15th, 2010, 11:54 AM   #3
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Re: Circle Problem

Beautiful!!! my only question is... why does A = B, or are we assuming this?
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November 15th, 2010, 12:09 PM   #4
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Re: Circle Problem

In order for the equation to describe a circle A = B is a requirement. If you take one of the general equations for a circle in the plane:

Expanding the squared binomials gives:

Now, multiplying through by any non-zero constant will still result in the coefficients of x and y being equal.
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