document.write( "Question 1167508: make an equation for the circle that goes through the points (9,2) , (-1,12), and (-9,-4) \n" ); document.write( "
Algebra.Com's Answer #792107 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Instead of doing your problem for you, I'll do a different one that is EXACTLY\r\n" );
document.write( "like yours step by step, that you can use as a guide for solving yours:\r\n" );
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document.write( "The one I'll solve is this one:\r\n" );
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Find an equation for the circle that goes through the points (2,12) , (-7,3), and (11,3)
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document.write( "The general equation of the circle is:\r\n" );
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document.write( "\"x%5E2%2By%5E2%2BAx%2BBy%2BC=0\"\r\n" );
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document.write( "Substituting (x,y) = (2,12)\r\n" );
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document.write( "\"%282%29%5E2%2B%2812%29%5E2%2BA%282%29%2BB%2812%29%2BC=0\"\r\n" );
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document.write( "\"4%2B144%2B2A%2B12B%2BC=0\"\r\n" );
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document.write( "\"148%2B2A%2B12B%2BC=0\"\r\n" );
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document.write( "\"2A%2B12B%2BC=-148\"\r\n" );
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document.write( "Substituting (x,y) = (-7,3)\r\n" );
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document.write( "\"%28-7%29%5E2%2B%283%29%5E2%2BA%28-7%29%2BB%283%29%2BC=0\"\r\n" );
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document.write( "\"49%2B9-7A%2B3B%2BC=0\"\r\n" );
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document.write( "\"58-7A%2B3B%2BC=0\"\r\n" );
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document.write( "\"-7A%2B3B%2BC=-58\"\r\n" );
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document.write( "Substituting (x,y) = (11,3)\r\n" );
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document.write( "\"%2811%29%5E2%2B%283%29%5E2%2BA%2811%29%2BB%283%29%2BC=0\"\r\n" );
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document.write( "\"121%2B9%2B11A%2B3B%2BC=0\"\r\n" );
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document.write( "\"130%2B11A%2B3B%2BC=0\"\r\n" );
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document.write( "\"11A%2B3B%2BC=-130\"\r\n" );
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document.write( "The system to solve is this:\r\n" );
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document.write( "\"system%282A%2B12B%2BC=-148%2C-7A%2B3B%2BC=-58%2C11A%2B3B%2BC=-130%29\"\r\n" );
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document.write( "Subtract the first two equations:\r\n" );
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document.write( "   2A+12B+C=-148\r\n" );
document.write( "-[-7A+ 3B+C= -58]\r\n" );
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document.write( "Change signs in bottom equation \r\n" );
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document.write( "  2A+12B+C=-148\r\n" );
document.write( "  7A- 3B-C=  58\r\n" );
document.write( "---------------\r\n" );
document.write( "  9A+ 9B  = -90\r\n" );
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document.write( "Subtract the first and third equations:\r\n" );
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document.write( "   2A+12B+C=-148\r\n" );
document.write( "-[11A+ 3B+C=-130]\r\n" );
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document.write( "  2A+12B+C=-148\r\n" );
document.write( "-11A- 3B-C= 130\r\n" );
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document.write( " -9A+ 9B  = -18\r\n" );
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document.write( "Solve the system:\r\n" );
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document.write( "\"system%28++9A%2B+9B++=+-90%2C-9A%2B+9B++=+-18%29\"\r\n" );
document.write( "        \r\n" );
document.write( "Add them term by term\r\n" );
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document.write( " 9A+9B=-90\r\n" );
document.write( "-9A+9B=-18\r\n" );
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document.write( "   18B=-108\r\n" );
document.write( "     B=-6  \r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "   9A+9B=-90\r\n" );
document.write( "9A+9(-6)=-90\r\n" );
document.write( "9A-54=-90\r\n" );
document.write( "   9A=-36\r\n" );
document.write( "    A=-4 \r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "2A+12B+C=-148\r\n" );
document.write( "2(-4)+12(-6)+C=-148\r\n" );
document.write( "  -8-72+C=-148\r\n" );
document.write( "    -80+C=-148\r\n" );
document.write( "        C=-68\r\n" );
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document.write( "So the equation of the circle \r\n" );
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document.write( "\"x%5E2%2By%5E2%2BAx%2BBy%2BC=0\"\r\n" );
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document.write( "becomes\r\n" );
document.write( "\"x%5E2%2By%5E2-4x-6y-68=0\"\r\n" );
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document.write( "Now do yours the EXACT same way.\r\n" );
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document.write( "Edwin
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