document.write( "Question 1069667: A circular vent pipe with a diameter of 5.6 inches is placed on a roof that has a slope of 1.1/1. The intersection of the vent pipe and the roof is an ellipse. What is the equation of the ellipse, with all values being written up to the 4th decimal place? \n" ); document.write( "
Algebra.Com's Answer #684825 by ikleyn(52831)\"\" \"About 
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\n" ); document.write( "A circular vent pipe with a diameter of 5.6 inches is placed on a roof that has a slope of 1.1/1.
\n" ); document.write( "The intersection of the vent pipe and the roof is an ellipse. What is the equation of the ellipse,
\n" ); document.write( "with all values being written up to the 4th decimal place?
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document.write( "I assume that the vent pipe is vertical and is cut by the roof's plane.\r\n" );
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document.write( "Then the major axis of the ellipse in the section is \"5.6%2Asqrt%281%5E2+%2B+1.1%5E2%29\" = \"5.6%2Asqrt%282.21%29\", and the major semi-axis is half of it: \r\n" );
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document.write( "a = \"%285.6%2F2%29%2Asqrt%282.21%29%29\" inches.    The minor semi-axis is b = \"5.6%2F2\" inches.\r\n" );
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document.write( "So, the ellipse equation in coordinates (x,y) in the coordinate plane coinciding with the roof surface is\r\n" );
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document.write( "\"x%5E2%2Fa%5E2+%2B+y%5E2%2Fb%5E2\" = 1,   which is the same as\r\n" );
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document.write( "\"x%5E2%2F%28%28%285.6%2F2%29%2Asqrt%282.21%29%29%5E2%29+%2B+y%5E2%2F%28%285.6%2F2%29%5E2%29\" = 1,    which is the same as\r\n" );
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document.write( "\"x%5E2%2F%282.8%5E2%2A2.21%29+%2B+y%5E2%2F2.8%5E2\" = 1,     which is the same as\r\n" );
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document.write( "\"x%5E2%2F17.3264+%2B+y%5E2%2F7.84\" = 1,    or, if you want ,\r\n" );
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document.write( "\"x%5E2%2F4.1625%5E2+%2B+y%5E2%2F2.8%5E2\" = 1.\r\n" );
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