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The circles (x+1)^2+(y-1)^2=9 and (x-3)^2+(y+1)^2=9 are overlapped. Find the point of intersections of the two circles.
\n" ); document.write( "solution
\n" ); document.write( "x^2+1+2x+y^2+1-2y=9 and x^2+9-6x+y^2+1+2y=9 both are equal to 9 by equalizing both circle
\n" ); document.write( "x^2+1+2x+y^2+1-2y= x^2+9-6x+y^2+1+2y
\n" ); document.write( "2x-2y+2=-6x+2y+10
\n" ); document.write( "x-y+1=-3x+y+5
\n" ); document.write( "4x=2y+4
\n" ); document.write( "2x=y+2 (1) y=2x-2 putting value in one equation of circle
\n" ); document.write( "(x+1)^2+(2x-3)^2=9
\n" ); document.write( "x^2+1+2x+4x^2+9-12x=9
\n" ); document.write( "5x^2-10x+10=9
\n" ); document.write( "5x^2-10x+1=0
\n" ); document.write( " centers are ( -1,1 ) and (3,-1 )
\n" ); document.write( " distance 2 sqre root 5 distance between both radius is less than sum of radius therefore both circle are intersecting
\n" ); document.write( "x=10+4sqr root5/10 or 10-4sqr root 5/10
\n" ); document.write( "x=1.89 or 0.105 \r
\n" ); document.write( "\n" ); document.write( "y=1.78 or y=-1.79
\n" ); document.write( "point of intersection will be (1.89,1.78) and (0.105,-1.79)\r
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