\r\n" );
document.write( "Because the x coordinate of (2a,a) is 2 times the y-coordinate,\r\n" );
document.write( "the set of points (2a,a) is the set of points in which \r\n" );
document.write( "each x coordinate is 2 times the y coordinate, which is\r\n" );
document.write( "\r\n" );
document.write( " x = 2y\r\n" );
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document.write( "So we draw the graphs of x²-2x-4y+3 = 0 and x = 2y\r\n" );
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document.write( "
\r\n" );
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document.write( "Since (2a,a) is INSIDE the parabola, we need to find the\r\n" );
document.write( "part of the line that is inside the parabola, so we need\r\n" );
document.write( "to find the points where the line intersects the parabola,\r\n" );
document.write( "by solving this system:\r\n" );
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document.write( "
\r\n" );
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document.write( "Solve this by substituting 2y for x in the first equation,\r\n" );
document.write( "and solving the resulting quadratic and we find the two\r\n" );
document.write( "points to be \r\n" );
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document.write( "
and 
\r\n" );
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document.write( "
\r\n" );
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document.write( "All the points on the line are of the form (2a,a), but\r\n" );
document.write( "We only want the points of the form (2a,a) that are inside the \r\n" );
document.write( "parabola. So we only want the part of the line which is between\r\n" );
document.write( "the two circles, this green part:\r\n" );
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document.write( "
\r\n" );
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document.write( "and the values of \"a\" and the values of \"x\" on the x-axis\r\n" );
document.write( "that are between 1 and 3:\r\n" );
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document.write( "
\r\n" );
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document.write( "answer: the interval {a|1 < a < 3} or (1,3) in interval notation.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
