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P_i and P'_i are the feet of perpendiculars from the foci S and S' onto a tangent T_i of an ellipse whose semi-major axis is 20. If the sum over i = 1 to 10 of (S P_i)(S' P'_i) equals 2560, find the value of 100e (e is the eccentricity).
- 60
- 80
- 120
- 40
Correct answer: 60
Solution
Each (S P_i)(S' P'_i) = b², so 10 b² = 2560 gives b² = 256; with a = 20, e = sqrt(1 - 256/400) = 0.6, so 100e = 60.
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