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Find the eccentricity of the ellipse that is the locus of midpoints of segments joining the fixed point (4, 3) to points on the ellipse x² + 2y² = 4.
- 1/sqrt(2)
- sqrt(3)/2
- 1/(2 sqrt(2))
- 1/2
Correct answer: 1/sqrt(2)
Solution
The midpoint locus is a translated, half-scaled copy of x² + 2y² = 4, which has a² = 4, b² = 2, giving e = sqrt(1 - 2/4) = 1/sqrt 2.
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