document.write( "Question 1087375: Show that the circles x^2 + y^2 - 16x - 20y + 115 = 0 and x^2 + y^2 + 8x - 10y + 5 = 0 are tangent and fine the point of tangency \n" ); document.write( "

Algebra.Com's Answer #701650 by Fombitz(32388) $\"\"$ $\"About$

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$\"x%5E2-16x%2By%5E2+-+20y+%2B+115+=+0\"$
\n" ); document.write( " $\"%28x-8%29%5E2%2B%28y-10%29%5E2=+-115%2B64%2B100+\"$
\n" ); document.write( " $\"%28x-8%29%5E2%2B%28y-10%29%5E2=49\"$
\n" ); document.write( " $\"%28x-8%29%5E2%2B%28y-10%29%5E2=7%5E2\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x%5E2%2B8x+%2B+y%5E2+-+10y+%2B+5+=+0\"$
\n" ); document.write( " $\"%28x%2B4%29%5E2%2B%28y-5%29%5E2=-5%2B16%2B25\"$
\n" ); document.write( " $\"%28x%2B4%29%5E2%2B%28y-5%29%5E2=36\"$
\n" ); document.write( " $\"%28x%2B4%29%5E2%2B%28y-5%29%5E2=6%5E2\"$
\n" ); document.write( "So the point of tangency lies on the line that connects the centers of the circles (8,10) and (-4,5).
\n" ); document.write( "If the distance from the centers is x then the point lies $\"%286%2F%286%2B7%29%29\"$ of the distance from (-4,5) to (8,10).
\n" ); document.write( "So the x distance from the centers is,
\n" ); document.write( " $\"dx=8-%28-4%29=12\"$
\n" ); document.write( "So then starting from -4,
\n" ); document.write( " $\"x%5Bt%5D=-4%2B12%286%2F13%29=-4%2B72%2F13=-52%2F13%2B72%2F13=20%2F13\"$
\n" ); document.write( "And the y distance is,
\n" ); document.write( " $\"dy=10-5=5\"$
\n" ); document.write( "And starting from 5,
\n" ); document.write( " $\"y%5Bt%5D=5%2B5%286%2F13%29=65%2F13%2B30%2F13=95%2F13\"$
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\n" ); document.write( "( $\"20%2F13\"$ , $\"95%2F13\"$ )
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