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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 = , and the major semi-axis is half of it:
a = inches. The minor semi-axis is b = inches.
So, the ellipse equation in coordinates (x,y) in the coordinate plane coinciding with the roof surface is
= 1, which is the same as
= 1, which is the same as
= 1, which is the same as
= 1, or, if you want ,
= 1.
Any of last two lines is your answer.