document.write( "Question 858395: What is the equation of a circle in general form whose center is at (-3,-4) and passes through the point (1,2)\r
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Algebra.Com's Answer #517197 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hi there,\r\n" );
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document.write( "Problem:\r\n" );
document.write( "What is the equation of a circle in general form whose center is at (-3,-4) and passes through the point (1,2)?\r\n" );
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document.write( "Solution:\r\n" );
document.write( "Begin with the equation for a circle in standard form where (a,b) is the center of the circle and r is its radius. \r\n" );
document.write( "\"%28x-a%29%5E2+%2B+%28y-b%29%5E2=r%5E2\"\r\n" );
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document.write( "We are given the center of the circle at (a,b)=(-3,-4), so our equation becomes\r\n" );
document.write( "\"%28x-%28-3%29%29%5E2+%2B+%28y-%28-4%29%29%5E2+=+r%5E2\"\r\n" );
document.write( "\"%28x%2B3%29%5E2+%2B+%28y%2B4%29%5E2+=+r%5E2\"\r\n" );
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document.write( "We all have a point (1,2) on the circle. Substitute 1 for x and 2 for y into the circle to find the radius r^2.\r\n" );
document.write( "\"%281%2B3%29%5E2+%2B+%282%2B4%29%5E2+=+r%5E2\"\r\n" );
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document.write( "This is the equation for our circle in standard form. The equation for a circle in general form looks like\r\n" );
document.write( "\"x%5E2%2By%5E2%2BAx%2BBy%2BC%2B0\"\r\n" );
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document.write( "To translate our equation to general form. Multiply everything out.\r\n" );
document.write( "\"x%5E2%2B6x%2B9%2By%5E2%2B8y%2B16=52\"\r\n" );
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document.write( "Subtract 36 from both sides and combine like terms. Then rearrange in the proper order.\r\n" );
document.write( "\"x%5E2%2B6x%2By%5E2%2B8y-27=0\"\r\n" );
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document.write( "The equation in general form is\r\n" );
document.write( "\"x%5E2%2By%5E2%2B6x%2B8y-27=0\"\r\n" );
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document.write( "Feel free to email me if your have questions about the solution.\r\n" );
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document.write( "~Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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