document.write( "Question 315555: Two circles x^2+y^2=11 and (x-3)^2+y^2=2 intersect at two points. P and Q. Find the exact length of the line segment PQ. \n" ); document.write( "

Algebra.Com's Answer #225766 by Fombitz(32388) $\"\"$ $\"About$

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Solve for the intersection points.
\n" ); document.write( " $\"x%5E2%2By%5E2=11\"$
\n" ); document.write( " $\"y%5E2=11-x%5E2\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"%28x-3%29%5E2%2By%5E2=2\"$
\n" ); document.write( " $\"%28x-3%29%5E2%2B%2811-x%5E2%29=2\"$
\n" ); document.write( " $\"x%5E2-6x%2B9%2B11-x%5E2=2\"$
\n" ); document.write( " $\"-6x%2B20=2\"$
\n" ); document.write( " $\"-6x=-18\"$
\n" ); document.write( " $\"highlight%28x=3%29\"$
\n" ); document.write( "Now solve for y
\n" ); document.write( " $\"y%5E2=11-x%5E2\"$
\n" ); document.write( " $\"y%5E2=11-9\"$
\n" ); document.write( " $\"y%5E2=2\"$
\n" ); document.write( " $\"highlight%28y=0+%2B-+sqrt%282%29%29\"$
\n" ); document.write( "Points P and Q are ( $\"3\"$ , $\"-sqrt%282%29\"$ ) and ( $\"3\"$ , $\"sqrt%282%29\"$ ).
\n" ); document.write( "The length of PQ is $\"2%2Asqrt%282%29\"$ .\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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