$\"\"$

A homeowner is putting in a fireplace that has a $\"\"$ inch-radius vent pipe.

He needs to cut an elliptical hole in his roof to accommodate the pipe.

The pitch of his roof is $\"\"$ .

Width of the pipe is $\"\"$ .

Length of the ellipse is calculated by $\"\"$ .

$\"\"$

Therefore, the elliptical hole will have a major length of $\"\"$ and minor length of $\"\"$ .

$\"\"$

Major length of the elliptical hole is $\"\"$ .

Minor length of the elliptical hole is $\"\"$ .