document.write( "Question 985218: Find the center and the radius of the circle that passes through the points (4,4) , (1,3) and (8,-4).
\n" ); document.write( "What are the coordinates of the center?\r
\n" ); document.write( "\n" ); document.write( "Thank you. \n" ); document.write( "
Algebra.Com's Answer #606053 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
\r
\n" ); document.write( "\n" ); document.write( "same as Question 985229\r
\n" ); document.write( "\n" ); document.write( "Find the center and the radius of the circle that passes through the points \r
\n" ); document.write( "\n" ); document.write( "(\"4\",\"4\") , (\"1\",\"3\") and (\"8\",\"-4\").\r
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\n" ); document.write( "\n" ); document.write( "equation of the circle is:\r
\n" ); document.write( "\n" ); document.write( "\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\" where \"h\" and \"k\" are \"x\" and \"y\" coordinates of the center, and \"r\" is radius\r
\n" ); document.write( "\n" ); document.write( "so use given points to set up system of three unknown
\n" ); document.write( "(\"4\",\"4\")
\n" ); document.write( "\"%284-h%29%5E2%2B%284-k%29%5E2=r%5E2\"....simplify\r
\n" ); document.write( "\n" ); document.write( "\"16-8h%2Bh%5E2%2B16-8k%2Bk%5E2=r%5E2\".............eq.1\r
\n" ); document.write( "\n" ); document.write( " (\"1\",\"3\")\r
\n" ); document.write( "\n" ); document.write( "\"%281-h%29%5E2%2B%283-k%29%5E2=r%5E2\"\r
\n" ); document.write( "\n" ); document.write( "\"1-2h%2Bh%5E2%2B9-6k%2Bk%5E2=r%5E2\".............eq.2\r
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\n" ); document.write( "\n" ); document.write( "(\"8\",\"-4\")\r
\n" ); document.write( "\n" ); document.write( "\"%288-h%29%5E2%2B%28-4-k%29%5E2=r%5E2\"....simplify\r
\n" ); document.write( "\n" ); document.write( "\"64-16h%2Bh%5E2%2B16%2B8k%2Bk%5E2=r%5E2\".............eq.3\r
\n" ); document.write( "\n" ); document.write( "start with
\n" ); document.write( "\"16-8h%2Bh%5E2%2B16-8k%2Bk%5E2=r%5E2\".............eq.1
\n" ); document.write( "\"64-16h%2Bh%5E2%2B16%2B8k%2Bk%5E2=r%5E2\".............eq.3
\n" ); document.write( "--------------------------------------------------------------------subtract\r
\n" ); document.write( "\n" ); document.write( "\"16-8h%2Bh%5E2%2B16-8k%2Bk%5E2-%2864-16h%2Bh%5E2%2B16%2B8k%2Bk%5E2%29=r%5E2-r%5E2\"
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\n" ); document.write( "\n" ); document.write( "\"-8h%2B16-8k-64%2B16h-8k=0\"\r
\n" ); document.write( "\n" ); document.write( "\"8h-16k=64-16\".......both sides divide by 8\r
\n" ); document.write( "\n" ); document.write( "\"h-2k=8-2\"\r
\n" ); document.write( "\n" ); document.write( "\"h-2k=6\"...............eg.1a\r
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\n" ); document.write( "\n" ); document.write( "go with
\n" ); document.write( "\"16-8h%2Bh%5E2%2B16-8k%2Bk%5E2=r%5E2\".............eq.1
\n" ); document.write( "\"1-2h%2Bh%5E2%2B9-6k%2Bk%5E2=r%5E2\".............eq.2
\n" ); document.write( "---------------------------------------------------------subtract\r
\n" ); document.write( "\n" ); document.write( "\"16-8h%2Bh%5E2%2B16-8k%2Bk%5E2-%281-2h%2Bh%5E2%2B9-6k%2Bk%5E2%29=r%5E2-r%5E2\"\r
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\n" ); document.write( "\n" ); document.write( "\"22-8h-8k%2B2h%2B6k=0\"\r
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\n" ); document.write( "\n" ); document.write( "\"-6h-2k=-22\"...............eg.2a\r
\n" ); document.write( "\n" ); document.write( "now go with
\n" ); document.write( "\"h-2k=6\"...............eg.1a
\n" ); document.write( "\"-6h-2k=-22\"...............eg.2a
\n" ); document.write( "-----------------------------------------------subtract \r
\n" ); document.write( "\n" ); document.write( "\"h-2k-%28-6h-2k%29=6-%28-22%29\"
\n" ); document.write( "\"h-cross%282k%29%2B6h%2Bcross%282k%29=6%2B22\"
\n" ); document.write( "\"h%2B6h=28\"
\n" ); document.write( "\"7h=28\"
\n" ); document.write( "\"h=28%2F7\"
\n" ); document.write( "\"highlight%28h=4%29\"\r
\n" ); document.write( "\n" ); document.write( "go to
\n" ); document.write( "\"h-2k=6\"...............eg.1a...plug in \"4\" for \"h\"\r
\n" ); document.write( "\n" ); document.write( "\"4-2k=6\"
\n" ); document.write( "\"4-6=2k\"
\n" ); document.write( "\"-2=2k\"
\n" ); document.write( "\"k=+-2%2F2\"
\n" ); document.write( "\"highlight%28k=+-1%29\"\r
\n" ); document.write( "\n" ); document.write( "go to\r
\n" ); document.write( "\n" ); document.write( "\"16-8h%2Bh%5E2%2B16-8k%2Bk%5E2=r%5E2\".............eq.1 ..plug in \"4\" for \"h\" and \"-1\" for \"k\" and find \"r\"\r
\n" ); document.write( "\n" ); document.write( "\"16-8%284%29%2B4%5E2%2B16-8%28-1%29%2B%28-1%29%5E2=r%5E2\"\r
\n" ); document.write( "\n" ); document.write( "\"cross%2816%29-cross%2832%29%2Bcross%2816%29%2B16%2B8%2B1=r%5E2\"\r
\n" ); document.write( "\n" ); document.write( "\"16%2B8%2B1=r%5E2\"\r
\n" ); document.write( "\n" ); document.write( "\"25=r%5E2\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28r=5%29\"\r
\n" ); document.write( "\n" ); document.write( "so, your equation is: \"%28x-4%29%5E2%2B%28y%2B1%29%5E2=25\" \r
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\n" ); document.write( "\n" ); document.write( "check:\r
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