document.write( "Question 1042977: $\"highlight%28A_circle_C%29\"$ x^2+y^2-2gx+2fy+e=0 has its center in the first quadrant. The x and y axes are tangents to C and
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Algebra.Com's Answer #658123 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( " $\"highlight%28A_circle_C%29\"$ x^2+y^2-2gx+2fy+e=0 has its center in the first quadrant. The x and y axes are tangents to C and
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document.write( "1.  Since the axes x- and y- are tangents to C, the center of C lies on the line x = y. (which is the diagonal of the QI).\r\n" );
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document.write( "    In other words, the center of the circle is at the point (x0,x0) for some x0 (now unknown).\r\n" );
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document.write( "2.  Due to the same reason, the radius of the circle is equal to x0 (and to y0, too).\r\n" );
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document.write( "3.  So, the equation of the circle is\r\n" );
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document.write( "     = .   (1)\r\n" );
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document.write( "    The point (3,6) lies on the circle, so coordinates satisfy the equation (1). In other words,\r\n" );
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document.write( "     = .\r\n" );
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document.write( "4.  It gives you a quadratic equation for .\r\n" );
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document.write( "     = .\r\n" );
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document.write( "    Simplify and solve for :\r\n" );
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document.write( "     = .\r\n" );
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document.write( "    The roots are   = 5  and   = 9.\r\n" );
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document.write( "5.  The first circle has the center (5,5) and the radius 5.\r\n" );
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document.write( "    Its equation is  = 25.\r\n" );
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document.write( "    The second circle has the center (9,9) and the radius 9.\r\n" );
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document.write( "    Its equation is  = 81.\r\n" );
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