The largest possible ellipse will have a semi-minor axis of 2 feet and a semi-major axis of 4 feet. If we center the board on the origin of the cartesian coordinate plane, we can derive the location of the foci and thus, the length of string he will need:
The slope is 3/10, and just graph 2 points ( so like .3,1 and .9,2) and just use Desmos to figure out the line using the y=3/10x+3.64 and just type it in
