document.write( "Question 1061422: find the center and radius of the circle having equation x^2+y^2+2x-4y+1=0 \n" ); document.write( "
Algebra.Com's Answer #676203 by Edwin McCravy(20059)\"\" \"About 
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\"x%5E2%2By%5E2%2B2x-4y%2B1=0\"
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document.write( "We need to get it in the form \"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\" so we'll\r\n" );
document.write( "know it has center (h,k) and radius r.\r\n" );
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document.write( "First we add -1 to both sides to get the constant off the left side:\r\n" );
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document.write( "\"x%5E2%2By%5E2%2B2x-4y=-1\"\r\n" );
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document.write( "Next we swap the 2nd and 3rd terms to get terms with the same letter\r\n" );
document.write( "next to each other:\r\n" );
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document.write( "\"x%5E2%2B2x%2By%5E2-4y=-1\"\r\n" );
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document.write( "Put the addition of one blank after the +2x and another after the \r\n" );
document.write( "-4y since we are going to add something to both sides:\r\n" );
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document.write( "\"x%5E2%2B2x%2B%22__%22%2By%5E2-4y%2B%22__%22=-1\"\r\n" );
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document.write( "Next we calculate what goes in the first blank:\r\n" );
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document.write( "1. Multiply the coefficient of x, which is 2, by \"1%2F2\"}, getting \"1\"\r\n" );
document.write( "2. Square that value:  \"%281%29%5E2+=+1\", so \"red%281%29\" is what goes\r\n" );
document.write( "in the first blank, and we also add it to the right side:\r\n" );
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document.write( "\"x%5E2%2B2x%2Bred%281%29%2By%5E2-4y%2B%22__%22=-1%2Bred%281%29\"  \r\n" );
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document.write( "Next we calculate what goes in the second blank:\r\n" );
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document.write( "1. Multiply the coefficient of y, which is -4, by \"1%2F2\"}, getting \"-2\"\r\n" );
document.write( "2. Square that value:  \"%28-2%29%5E2+=+%22%2B4%22\", so \"red%284%29\" is \r\n" );
document.write( "what goes in the second blank, and we also add it to the right \r\n" );
document.write( "side:\r\n" );
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document.write( "\"x%5E2%2B2x%2Bred%281%29%2By%5E2-4y%2Bred%284%29=-1%2Bred%281%29%2Bred%284%29\"\r\n" );
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document.write( "The first three terms on the left \"x%5E2%2B2x%2B1\" factors as \"%28x%2B1%29%28x%2B1%29\" \r\n" );
document.write( "or \"%28x%2B1%29%5E2\"\r\n" );
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document.write( "The last three terms on the left \"y%5E2-4y%2B4\" factors as \"%28y-2%29%28y-2%29\" \r\n" );
document.write( "or \"%28y-2%29%5E2\"\r\n" );
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document.write( "The right side \"-1%2B1%2B4\" becomes \"4\"\r\n" );
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document.write( "So we now have:\r\n" );
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document.write( "\"%28x%2B1%29%5E2%2B%28y-2%29%5E2=4\"\r\n" );
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document.write( "And we compare that to \r\n" );
document.write( "\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\" \r\n" );
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document.write( "and we see that since \"-h=%22%22%2B1%22\", \"h=-1\", and\r\n" );
document.write( "since \"-k=-2\", \"k=2\". Also \"r%5E2=4\" so \"r=sqrt%284%29=2\"}\r\n" );
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document.write( "So the center is (h,k) = (-1,2) and the radius = r = 2.\r\n" );
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document.write( "Edwin

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