Question 1069667
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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?
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I assume that the vent pipe is vertical and is cut by the roof's plane.


Then the major axis of the ellipse in the section is {{{5.6*sqrt(1^2 + 1.1^2)}}} = {{{5.6*sqrt(2.21)}}}, and the major semi-axis is half of it: 


a = {{{(5.6/2)*sqrt(2.21))}}} inches.    The minor semi-axis is b = {{{5.6/2}}} inches.


So, the ellipse equation in coordinates (x,y) in the coordinate plane coinciding with the roof surface is


{{{x^2/a^2 + y^2/b^2}}} = 1,   which is the same as


{{{x^2/(((5.6/2)*sqrt(2.21))^2) + y^2/((5.6/2)^2)}}} = 1,    which is the same as


{{{x^2/(2.8^2*2.21) + y^2/2.8^2}}} = 1,     which is the same as


{{{x^2/17.3264 + y^2/7.84}}} = 1,    or, if you want ,


{{{x^2/4.1625^2 + y^2/2.8^2}}} = 1.
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Any of last two lines is your answer.