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Find the equation of a circle tangant to the axes and passing through (2,1)
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\n" ); document.write( "The equation for a circle with center (a,b) and radius R is (x-a)^2 + (y-b)^2 = R^2\r
\n" ); document.write( "\n" ); document.write( "If the circle is tangent to both axes, then the points of tangency are (R,0) and (0,R)
\n" ); document.write( "Therefore, the circle must be centered at the point (R,R)
\n" ); document.write( "The circle passes through the point (2,1):
\n" ); document.write( "(2-R)^2 + (1-R)^2 = R^2
\n" ); document.write( "Solve for R:
\n" ); document.write( "4 - 4R + R^2 + 1 - 2R + R^2 = R^2
\n" ); document.write( "R^2 - 6R + 5 = 0
\n" ); document.write( "(R-5)(R-1) = 0
\n" ); document.write( "This gives two solutions, R=1 and R=5
\n" ); document.write( "So there are two circles which satisfy the requirements:
\n" ); document.write( "(x-1)^2 + (y-1)^2 = 1
\n" ); document.write( "(x-5)^2 + (y-5)^2 = 25
\n" ); document.write( "The circles are graphed below. Note that both circles pass through the point (2,1)
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