document.write( "Question 1031604: find the equation of a circle passing through the points (-3,6),(-5,2),(3,-6) \n" ); document.write( "
Algebra.Com's Answer #646277 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "The standard equation of a circle is\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "Substituting the three points we have this system:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplifying and rearranging the terms:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Subtracting the third equation from the first:\r\n" );
document.write( "\r\n" );
document.write( "\"12h-24k=0\"\r\n" );
document.write( "\"h-2k=0\"\r\n" );
document.write( "\"h=2k\"\r\n" );
document.write( "\r\n" );
document.write( "Subtracting the second equation from the first:\r\n" );
document.write( "\r\n" );
document.write( "\"-4h-8k%2B16=0\"\r\n" );
document.write( "\"h%2B2k-4=0\"\r\n" );
document.write( "\r\n" );
document.write( "Substituting 2k for h\r\n" );
document.write( "\r\n" );
document.write( "\"2k%2B2k-4=0\"\r\n" );
document.write( "\"4k-4=0\"\r\n" );
document.write( "\"4k=4\"\r\n" );
document.write( "\"h=1\"\r\n" );
document.write( "\r\n" );
document.write( "So the center = (h,k) = (2,1)\r\n" );
document.write( "\r\n" );
document.write( "Substituting h=2 and k=1 in the first equation\r\n" );
document.write( "\r\n" );
document.write( "\"h%5E2%2B6h%2Bk%5E2-12k%2B45=r%5E2\"\r\n" );
document.write( "\"2%5E2%2B6%282%29%2B1%5E2-12%281%29%2B45=r%5E2\"\r\n" );
document.write( "\"4%2B12%2B1-12%2B45=r%5E2\"\r\n" );
document.write( "\"50=r%5E2\"\r\n" );
document.write( "\"sqrt%2850%29=r\"\r\n" );
document.write( "\"5sqrt%282%29=r\"\r\n" );
document.write( "\r\n" );
document.write( "The equation\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\" becomes\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-2%29%5E2%2B%28y-1%29%5E2=50\"\r\n" );
document.write( "\r\n" );
document.write( "Or if you multiply that out and get the general form:\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2%2By%5E2-4x-2y%2B45=0\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "
\n" );