document.write( "Question 1206482: Given the two circles defined by the equations x^(2)-6x+y^(2)+8y=12 and x^(2)+y^(2)=4y, find the algebraic equation of the line connecting their centers. \n" ); document.write( "

Algebra.Com's Answer #843995 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Given the two circles defined by the equations x^(2)-6x+y^(2)+8y=12 and x^(2)+y^(2)=4y,
\n" ); document.write( "find the algebraic equation of the line connecting their centers.
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document.write( "To find the centers, apply completing the squares separately to x-terms and y-terms in each equation.\r\n" );
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document.write( "                It can be done MENTALLY.\r\n" );
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document.write( "The center of the 1st circle is the point (3,-4).\r\n" );
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document.write( "The center of the 2nd circle is the point (0,2).\r\n" );
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document.write( "The slope of the line through the centers is  m =  =  = -2.\r\n" );
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document.write( "So, an equation of the line can be presented in the form\r\n" );
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document.write( "    y-2 = m*(x-0),\r\n" );
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document.write( "or\r\n" );
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document.write( "    y - 2 = -2x,  or  y = -2x + 2,\r\n" );
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document.write( "or in any other equivalent form.\r\n" );
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document.write( "You can check on your own that the presented equations are satisfied with\r\n" );
document.write( "the coordinates of the centers, so this straight line goes through these points.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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