November 13th, 2010, 12:36 PM  #1 
Senior Member Joined: Apr 2009 Posts: 106 Thanks: 0  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.

November 13th, 2010, 03:57 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Circle Problem Hello, julian21! I'll give this a try . . . Quote:
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November 15th, 2010, 11:54 AM  #3 
Senior Member Joined: Apr 2009 Posts: 106 Thanks: 0  Re: Circle Problem
Beautiful!!! my only question is... why does A = B, or are we assuming this?

November 15th, 2010, 12:09 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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 nonzero constant will still result in the coefficients of x² and y² being equal. 

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