document.write( "Question 1186881: What is the equation of the ellipse having major axis of length 12, center at
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Algebra.Com's Answer #817927 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Instead of doing yours for you, I'll do one exactly like yours step by step, so\r\n" );
document.write( "you can use it as a model to do yours by.  Here is the problem I will do.\r\n" );
document.write( "Just use your numbers instead of the ones here:\r\n" );
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document.write( "What is the equation of the ellipse having major axis of length 16, center at\r\n" );
document.write( "(-3,-8), and a focus at (4,-8)?\r\n" );
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document.write( "The equation of an ellipse with major axis horizontal is\r\n" );
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document.write( "\"%28x-h%29%5E2%2Fa%5E2\"\"%22%22%2B%22%22\"\"%28y-k%29%5E2%2Fb%5E2\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "where the center is (h,k) = (-3,-8), and where \"a\" = semi-major axis length.\r\n" );
document.write( "The major axis is 16, so the semi-major axis = 8. So far we have\r\n" );
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document.write( "\"%28x-%28-3%29%29%5E2%2F%288%29%5E2\"\"%22%22%2B%22%22\"\"%28y-%28-8%29%29%5E2%2Fb%5E2\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "\"%28x%2B3%29%5E2%2F64\"\"%22%22%2B%22%22\"\"%28y%2B8%29%5E2%2Fb%5E2\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "We need \"b\", which is the semi-minor axis length.  We have to use the\r\n" );
document.write( "Pythagorean theorem relationship for all ellipses, which is\r\n" );
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document.write( "\"c%5E2\"\"%22%22=%22%22\"\"a%5E2\"\"%22%22-%22%22\"\"b%5E2\"\r\n" );
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document.write( "where c = distance from center to a focus.  The distance from the center (-3,-8)\r\n" );
document.write( "to the focus, which is (4,-8) is 7 units, found by counting units on the graph\r\n" );
document.write( "above.  So b = 7, and the complete equation of the ellipse is\r\n" );
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document.write( "\"%28x%2B3%29%5E2%2F64\"\"%22%22%2B%22%22\"\"%28y%2B8%29%5E2%2F7%5E2\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "\"%28x%2B3%29%5E2%2F36\"\"%22%22%2B%22%22\"\"%28y%2B8%29%5E2%2F49\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "Now do yours exactly, step by step, like this one.\r\n" );
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document.write( "Edwin
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