document.write( "Question 992326: Please help me with this! Show that the two circles (x - 3)^2 + (y-4)^2 = 25 and (x-1)^2 + (y-5/2)^2 =225/4. touch each other. \n" ); document.write( "

Algebra.Com's Answer #611973 by Edwin McCravy(20055) $\"\"$ $\"About$

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$\"%28x-3%29%5E2+%2B+%28y-4%29%5E2+=+25\"$
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document.write( "Subtract the two equations to get the equation of the line through\r\n" );
document.write( "their point(s) of intersection if they have any points in common. \r\n" );
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document.write( "Factor first two and last two terms on the left as the\r\n" );
document.write( "difference of squares:\r\n" );
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document.write( "Multiply through by 4\r\n" );
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document.write( "Divide through by -4\r\n" );
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document.write( "This is the equation of the line through their\r\n" );
document.write( "point(s) of intersection if the intersect. \r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "Multiply through by 9\r\n" );
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document.write( "Divide through by 25\r\n" );
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document.write( "That give the double solution x=7.  The double solution\r\n" );
document.write( "means that the circles intersect at one point, where x=7.\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "Therefore they intersect at the one point (7,7)\r\n" );
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document.write( "Edwin

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