When constructing an ellipse, the length of the string is

• A. 2 times the major axis
• B. 2 times the semi-major axis
• C. 2 times the minor axis
• D. 2 times the semi-minor axis

Answer: (B)

In an ellipse, the sum of the distances from any point on the curve to the two foci is constant, and that constant equals the length of the major axis. When you construct an ellipse with a string and two pins, the string stays taut with that fixed sum of distances, so its length must be the major axis length. Since the major axis is twice the semi-major axis, the string length is two times the semi-major axis. The minor axis describes the ellipse’s width at the center and isn’t tied to the fixed string length, so it isn’t the value you’re using for the string.