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Let S and S' be the foci of an ellipse and let B be an extremity of its minor axis. The triangle S'BS is right-angled at B and has area 8 square units. Find the length of the latus rectum of the ellipse.

1. 4
2. 2*sqrt(2)
3. 2
4. 4*sqrt(2)

Correct answer: 4

Solution

Right angle at B forces b = c, so the area = (1/2)(SS')(b) = c*b = b² = 8, giving b² = 8; latus rectum = 2b²/a with a² = b² + c² = 2b², a = b*sqrt(2), so LR = 2b²/(b*sqrt2) = b*sqrt2 = 4.

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