Algebra.Com's Answer #696014 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Find equation when the center on the line x - 2y - 9 = 0 and passes through the points (7,-2) and (5,0).
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document.write( "The center of the circle lies on the perpendicular bisector to the segment connecting the points (7,-2) and (5,0).\r\n" );
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document.write( "The midpoint is (6,-1). (6 =  , -1 =  )\r\n" );
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document.write( "The segment connecting the given points has the slope  =  = -1.\r\n" );
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document.write( "Therefore, the perpendicular bisector has the slope 1.\r\n" );
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document.write( "Hence, the perpendicular bisector passing through the point (6,-1) has the equation\r\n" );
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document.write( "y - (-1) = 1*(x-6), or, which is the same, y+1 = x - 6.\r\n" );
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document.write( "Hence, the center of the circle lies at the intersection of these two lines\r\n" );
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document.write( "x - 2y - 9 = 0 (1) and\r\n" );
document.write( "y+1 = x - 6. (2)\r\n" );
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document.write( "This system is the same as\r\n" );
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document.write( "x - 2y = 9, (3)\r\n" );
document.write( "x - y = 7. (4)\r\n" );
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document.write( "To solve the system (and to find the intersection point) subtract (4) from (3) both sides). You will get\r\n" );
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document.write( "-y = 2, or y = -2.\r\n" );
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document.write( "Then x = 7 + y = 7 + (-2) = 5 (from (4).\r\n" );
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document.write( "Thus the point (5,-2) is the center.\r\n" );
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document.write( "The distance from the center (5,-2) to the given point (5,0) is  =  =  = 2.\r\n" );
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document.write( "Then the equation of the circle is \r\n" );
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document.write( " = 4, or\r\n" );
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document.write( " = 4.\r\n" );
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document.write( "Solved.\r
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document.write( "The solution by \"josgarithmetic\" is WRONG.\r
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