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Two ellipses are E1: x²/3 + y²/2 = 1 and E2: x²/16 + y²/b² = 1. If the product of their eccentricities is 1/2, find a possible value for the length of the minor axis of E2.
- 8
- 9
- 2
- 4
Correct answer: 8
Solution
e1 = 1/sqrt(3) forces e2 = sqrt(3)/2; if E2 has its major axis along the y-axis then the term 16 becomes the minor semi-axis squared, giving minor-axis length 8.
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