document.write( "Question 1079015: Find the equation of the circle that passes through the origin and (2,4); tangent to the line 3x - 2y = 12. \n" ); document.write( "

Algebra.Com's Answer #693473 by ikleyn(52855) $\"\"$ $\"About$

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\n" ); document.write( "Find the equation of the circle that passes through the origin and (2,4); tangent to the line 3x - 2y = 12.
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document.write( "According to the condition, the circle passes through the points (0,0) and (2,4).\r\n" );
document.write( "Therefore, its center lies on the perpendicular bisector of the segment connecting these points.\r\n" );
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document.write( "     Now, the idea on how to solve the problem is to find the point on the perpendicular bisector EQUIDISTANT from the given points \r\n" );
document.write( "          AND from the given straight line.\r\n" );
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document.write( "The midpoint between (0,0) and (2,4) is the point (1,2).\r\n" );
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document.write( "The slope of the segment connecting (0,0) and (2,4) is  = 2.\r\n" );
document.write( "Hence, the slope of the perpendicular bisector is .\r\n" );
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document.write( "Thus the equation of the perpendicular bisector passing through (1,2) is\r\n" );
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document.write( "y - 2 = \r\n" );
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document.write( "From the other side, the distance from the point (x,y) to the given straight line 3x - 2y = 12 is equal to\r\n" );
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document.write( "d =  =  = ,\r\n" );
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document.write( "according to the lesson The distance from a point to a straight line in a coordinate plane in this site.\r\n" );
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document.write( "Therefore, the center of the circle lies on the straight line\r\n" );
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document.write( "y - 2 = \r\n" );
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document.write( "and is equidistant from the point (0,0) and the straight line 3x-2y - 12 = 0, which means\r\n" );
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document.write( " = .\r\n" );
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document.write( "Thus the problem is reduced to solving this system of equations\r\n" );
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document.write( "y - 2 =         (1)     and\r\n" );
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document.write( " = .     (2)\r\n" );
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document.write( "The setup is done. The rest is just technique.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Writing of \"josgarithmetic\" on this problem is wrong and irrelevant.\r
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