document.write( "Question 1204202: 36x^2+25y^2-288x+200y+76=0 is the equation of a conic. Write the standard form of that conic. \n" ); document.write( "

Algebra.Com's Answer #840297 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "Get the x terms together and the y-terms together and\r\n" );
document.write( "the constant term on the right\r\n" );
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document.write( "Factor the coefficient of the squared terms out of the first two terms\r\n" );
document.write( "and the last two terms on the left:\r\n" );
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document.write( "We want to add a positive number inside each parentheses to make\r\n" );
document.write( "it factorable as a perfect square.  To find that number\r\n" );
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document.write( "In the first parentheses,\r\n" );
document.write( "Half the coefficient of x, which is -8, getting -4, then square\r\n" );
document.write( "-4 getting +16 and add that inside the first parentheses on the right. Since \r\n" );
document.write( "there is a coefficient of 36, adding +16 inside the first parentheses is\r\n" );
document.write( "the equivalent of adding 36x16 or 576 to the left side. So we must add\r\n" );
document.write( "576 to the right side as well:\r\n" );
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document.write( "In the second parentheses,\r\n" );
document.write( "Half the coefficient of y, which is +8, getting +4, then square\r\n" );
document.write( "+4 getting +16 and add that inside the second parentheses on the right. Since \r\n" );
document.write( "there is a coefficient of 25, adding +16 inside the second parentheses is\r\n" );
document.write( "the equivalent of adding 25x16 or 400 to the left side. So we must add\r\n" );
document.write( "400 to the right side as well:\r\n" );
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document.write( "Now we factor each parentheses and combine the numbers on the right side.\r\n" );
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document.write( "We notice that they factored into perfect squares, so perhaps you can skip\r\n" );
document.write( "the preceding step, and have gone straight to\r\n" );
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document.write( "Now we must get 1 on the right side, so we divide through by 900\r\n" );
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document.write( "The coefficients of the squares of binomials must be 1, so divide\r\n" );
document.write( "the top and bottom of the first term by 36 and the second by 25.\r\n" );
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document.write( " compare to \r\n" );
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document.write( "That's a vertical ellipse (looks like the number \"0\") because the larger\r\n" );
document.write( "denominator a² is under the term in y.  \r\n" );
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document.write( "It has center (h,k)=(4,-4). \r\n" );
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document.write( "It has semi-major axis a=6, semi-minor axis b=5.\r\n" );
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document.write( "Vertices (4,-10) and (4,2) and co-vertices (-1,-4) and (9,-4).\r\n" );
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document.write( "Edwin

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