document.write( "Question 154264: rotation of axes question.\r
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\n" ); document.write( "\n" ); document.write( "write equation in terms of rotated x' y' system using theta, the angle of rotation. Write the equation ?
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\n" ); document.write( "\n" ); document.write( "\"13x%5E2-10xy%2B13y%5E2-72=0\"; θ = 45° \n" ); document.write( "
Algebra.Com's Answer #113592 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
rotation of axes question.
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document.write( "write equation in terms of rotated x' y' system using theta, \r\n" );
document.write( "the angle of rotation. Write the equation involving x' y' \r\n" );
document.write( "in standard form.\r\n" );
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document.write( "\"13x%5E2-10xy%2B13y%5E2-72=0\"; θ = 45°\r\n" );
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document.write( "If a locus is defined on the xy-coordinate system as , then \r\n" );
document.write( "it is denoted as on the rotated x'y'-coordinate system.\r\n" );
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document.write( "We calculate the substitutions to make:\r\n" );
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document.write( "x = x'cosθ-y'sinθ,  \r\n" );
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document.write( "y = x'sinθ+y'cosθ\r\n" );
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document.write( "x = x'\"%28sqrt%282%29%2F2%29\"-y'\"%28sqrt%282%29%2F2%29\" = \"sqrt%282%29%2F2\"(x'-y')\r\n" );
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document.write( "y = x'\"%28sqrt%282%29%2F2%29\"+y'\"%28sqrt%282%29%2F2%29\" = \"sqrt%282%29%2F2\"(x'+y')\r\n" );
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document.write( "x² = \"%28sqrt%282%29%2F2%29%5E2\"(x'-y')² = \"2%2F4\"(x'²-2x'y'+y'²}=\"1%2F2\"(x'²-2x'y'+y'²}\r\n" );
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document.write( "xy = \"sqrt%282%29%2F2\"(x'-y')\"sqrt%282%29%2F2\"(x'+y')=\"2%2F4\"(x'-y')(x'+y')=\"1%2F2\"(x'²-y'²)\r\n" );
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document.write( "y² = \"%28sqrt%282%29%2F2%29%5E2\"(x'+y')² = \"2%2F4\"(x'²+2x'y'+y'²}=\"1%2F2\"(x'²+2x'y'+y'²}\r\n" );
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document.write( "\"13x%5E2-10xy%2B13y%5E2-72=0\"\r\n" );
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document.write( "\"%2813%29\"·\"1%2F2\"(x'²-2x'y'+y'²}-\"%2810%29\"·\"1%2F2\"(x'²-y'²)+\"%2813%29\"·\"1%2F2\"(x'²+2x'y'+y'²}-72=0\r\n" );
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document.write( "\"13%2F2\"·(x'²-2x'y'+y'²}-\"10%2F2\"·(x'²-y'²)+\"13%2F2\"·(x'²+2x'y'+y'²}-72=0\r\n" );
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document.write( "Clear of fractions by multiplying through by 2:\r\n" );
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document.write( " 13(x'²-2x'y'+y'²}-10(x'²-y'²)+13(x'²+2x'y'+y'²}-144=0\r\n" );
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document.write( "13x'²-26x'y'+13y'²-10x'²+10y'²+13x'²+26x'y'+13y'²-144=0\r\n" );
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document.write( "                                      16x'²+36y'²-144 = 0\r\n" );
document.write( "Divide through by 4\r\n" );
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document.write( "                                       4x'²+9y'²-36=0\r\n" );
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document.write( "                                          4x'²+9y'²=36\r\n" );
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document.write( "Divide through by 36:\r\n" );
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document.write( "                                   \r\n" );
document.write( "                                    \"%284x%5E%22%27%22%29%5E2%2F36%2B9%28y%5E%22%27%22%29%5E2%2F36=36%2F36\"\r\n" );
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document.write( "                                    \"%28x%5E%22%27%22%29%5E2%2F9%2B%28y%5E%22%27%22%29%5E2%2F4=1\"\r\n" );
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document.write( "Edwin
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