A furniture maker has a rectangular block of wood that measures 37.5 inches by 25 inches. He wants to cut it to make the largest elliptical table top possible. Find an equation of the ellipse he can use, placing the center at the origin and the major axis on the x-axis. Locate the approximate foci of the ellipse.

Question

Mathematics

Johnston

23 October, 13:00

A furniture maker has a rectangular block of wood that measures 37.5 inches by 25 inches. He wants to cut it to make the largest elliptical table top possible. Find an equation of the ellipse he can use, placing the center at the origin and the major axis on the x-axis. Locate the approximate foci of the ellipse.

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Diamond Webb · Answer 1

The largest ellipse that will fit in that table will be:

(x / (37.5/2)) ^2 + (y / (25/2)) ^2=1

(x/18.75) ^2 + (y/12.5) ^2=1

The foci will be at:

±c^2=a^2-b^2

±c^2 = (18.75) ^2 - (12.5) ^2

±c^2=195.3125

±c≈13.975

So the foci will be at approximately (-14,0) and (14,0)