document.write( "Question 1015551: please help me graph 3x^2 + 4y^2 -6x -24y +39=0 \n" ); document.write( "
Algebra.Com's Answer #631892 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"3x%5E2%2B4y%5E2-6x-24y%2B39=0\"\r\n" );
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document.write( "This appears to be the equation of an ellipse:\r\n" );
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document.write( "\"3x%5E2-6x%2B4y%5E2-24y=-39\"\r\n" );
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document.write( "\"3%28x%5E2-2x%29%2B4%28y%5E2-6y%29=-39\"\r\n" );
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document.write( "Complete the square in the first parentheses on the left:\r\n" );
document.write( "Coefficient of x is -2\r\n" );
document.write( "Multiply it by 1/2, get -1\r\n" );
document.write( "Square that: (-1)2 = +1\r\n" );
document.write( "Add +1-1 inside the first parentheses on the end:\r\n" );
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document.write( "\"3%28x%5E2-2x%2B1-1%29%2B4%28y%5E2-6y%29=-39\"\r\n" );
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document.write( "Complete the square in the second parentheses on the left:\r\n" );
document.write( "Coefficient of y is -6\r\n" );
document.write( "Multiply it by 1/2, get -3\r\n" );
document.write( "Square that: (-3)2 = +9\r\n" );
document.write( "Add +9-9 inside the second parentheses on the end:\r\n" );
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document.write( "\"3%28x%5E2-2x%2B1-1%29%2B4%28y%5E2-6y%2B9-9%29=-39\"\r\n" );
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document.write( "Factor the first three terms in each parentheses as\r\n" );
document.write( "the square of a binomial:\r\n" );
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document.write( "\"3%28%28x-1%29%5E2-1%29%2B4%28%28y-3%29%5E2-9%29=-39\"\r\n" );
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document.write( "Distribute the 3 and 4 into the outer parentheses \r\n" );
document.write( "leaving the two squares of binomials intact:\r\n" );
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document.write( "\"3%28x-1%29%5E2-3%2B4%28y-3%29%5E2-36=-39\"\r\n" );
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document.write( "\"3%28x-1%29%5E2%2B4%28y-3%29%5E2-39=-39\"\r\n" );
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document.write( "\"3%28x-1%29%5E2%2B4%28y-3%29%5E2=0\"\r\n" );
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document.write( "Normally we don't get a 0 on the right, and we divide\r\n" );
document.write( "through by what we get.  But this is a rare case.  We\r\n" );
document.write( "cannot divide by 0.  \r\n" );
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document.write( "Both terms are non-negative, so the left side must be 0.  \r\n" );
document.write( "It can only be 0 if x=1 and y=3.\r\n" );
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document.write( "So this is the equation of the point (1,3).  It is really\r\n" );
document.write( "an ellipse so small it has shrunk down to a point!\r\n" );
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document.write( "Here is the graph (Yes, that's all there is to it! One point!)\r\n" );
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document.write( "Edwin
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