a rectangular board is 2 by 12 units. How far from the short sides of the board will the foci be located to determine the largest elliptical tabletop?

Question

a rectangular board is 2 by 12 units. How far from the short sides of the board will the foci be located to determine the largest elliptical tabletop

Clearly, the largest elliptical tabletop will have a semi-major axis a = 6 and a semi-minor axis b =1.

The distance of the foci from the center of the ellipse derives from c = sqrt(a^2 - b^2 = sqrt(36 - 1) = 5.916 making the distance of both foci from each end .0839 units.