document.write( "Question 1208377: Find the equation of the circle passing through the points (1,2),(3,6),(5,4).\r
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Algebra.Com's Answer #846780 by MathTherapy(10552)\"\" \"About 
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document.write( "Find the equation of the circle passing through the points (1,2),(3,6),(5,4).\r\n" );
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document.write( "We start with: \"matrix%281%2C3%2C+%28x++-++h%29%5E2+%2B+%28y+-+k%29%5E2%2C+%22=%22%2C+r%5E2%29\" <==== Standard form of the equation of a CIRCLE: \r\n" );
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document.write( "           Point: (1, 2)\r\n" );
document.write( "          \"matrix%281%2C3%2C+%28x++-++h%29%5E2+%2B+%28y+-+k%29%5E2%2C+%22=%22%2C+r%5E2%29\" ---- Standard form of the equation of a CIRCLE\r\n" );
document.write( "          \"matrix%281%2C3%2C+%281++-++h%29%5E2+%2B+%282+-+k%29%5E2%2C+%22=%22%2C+r%5E2%29\" ---- Substituting (1, 2) for (x, y) \r\n" );
document.write( "1 - 2h + h2 + 4 - 4k + k2 = r2\r\n" );
document.write( "    h2 - 2h + k2 - 4k + 5 = r2 ----- eq (i)\r\n" );
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document.write( "            Point: (3, 6)\r\n" );
document.write( "            \"matrix%281%2C3%2C+%28x++-++h%29%5E2+%2B+%28y+-+k%29%5E2%2C+%22=%22%2C+r%5E2%29\" ---- Standard form of the equation of a CIRCLE\r\n" );
document.write( "            \"matrix%281%2C3%2C+%283++-++h%29%5E2+%2B+%286+-+k%29%5E2%2C+%22=%22%2C+r%5E2%29\" ---- Substituting (3, 6) for (x, y) \r\n" );
document.write( "9 - 6h + h2 + 36 - 12k + k2 = r2\r\n" );
document.write( "    h2 - 6h + k2 - 12k + 45 = r2 ----- eq (ii)\r\n" );
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document.write( "            Point: (5, 4)\r\n" );
document.write( "            \"matrix%281%2C3%2C+%28x++-++h%29%5E2+%2B+%28y+-+k%29%5E2%2C+%22=%22%2C+r%5E2%29\" ---- Standard form of the equation of a CIRCLE\r\n" );
document.write( "            \"matrix%281%2C3%2C+%285++-++h%29%5E2+%2B+%284+-+k%29%5E2%2C+%22=%22%2C+r%5E2%29\" ---- Substituting (5, 4) for (x, y) \r\n" );
document.write( "25 - 10h + h2 + 16 - 8k + k2 = r2\r\n" );
document.write( "     h2 - 10h + k2 - 8k + 41 = r2 ----- eq (iii)\r\n" );
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document.write( "       h2 - 2h + k2 - 4k + 5 = r2 ----- eq (i)\r\n" );
document.write( "     h2 - 6h + k2 - 12k + 45 = r2 ----- eq (ii)\r\n" );
document.write( "     h2 - 10h + k2 - 8k + 41 = r2 ----- eq (iii)\r\n" );
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document.write( "              4h + 8k  -  40 = 0 ----- Subtracting eq (ii) from eq (i)\r\n" );
document.write( "                     4h + 8k = 40\r\n" );
document.write( "                   4(h + 2k) = 4(10)\r\n" );
document.write( "                      h + 2k = 10 ---- eq (iv)\r\n" );
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document.write( "                 4h - 4k + 4 = 0 ----- Subtracting eq (iii) from eq (ii)\r\n" );
document.write( "                     4h - 4k = - 4\r\n" );
document.write( "                    4(h - k) = 4(- 1)\r\n" );
document.write( "                       h - k = - 1 --- eq (v)\r\n" );
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document.write( "                      h + 2k = 10 ---- eq (iv)\r\n" );
document.write( "                       h - k = - 1 --- eq (v)\r\n" );
document.write( "                          3k = 11 ---- Subtracting eq (v) from eq (iv)\r\n" );
document.write( "                          \"matrix%281%2C3%2C+k%2C+%22=%22%2C++11%2F3%29\"\r\n" );
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document.write( "                    h - \"11%2F3\" = - 1 ---- Substituting \"11%2F3\" for k in eq (v) \r\n" );
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document.write( "        (x - h)2 + (y - k)2 = r2\r\n" );
document.write( "         \"matrix%281%2C3%2C+%281++-++8%2F3%29%5E2+%2B+%282++-++11%2F3%29%5E2%2C+%22=%22%2C+r%5E2%29\" -- Substituting (1, 2) for (x, y), and (\"matrix%281%2C3%2C+8%2F3%2C+%22%2C%22%2C+11%2F3%29\") for (h, k)\r\n" );
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document.write( "            \"matrix%281%2C3%2C+%28x++-++h%29%5E2+%2B+%28y+-+k%29%5E2%2C+%22=%22%2C+r%5E2%29\" <==== Standard form of the equation of a CIRCLE\r\n" );
document.write( "         --- Substituting (\"matrix%281%2C3%2C+8%2F3%2C+%22%2C%22%2C+11%2F3%29\") for (h, k), and \"50%2F9\" for r2
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