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A focal chord of the parabola y² = 4x makes an angle alpha (with alpha in (0, pi/4]) with the positive x-axis. Find the minimum possible length of such a focal chord.
- 2*sqrt(2)
- 4*sqrt(2)
- 8
- 16
Correct answer: 8
Solution
Focal chord length = 4a*cosec²(alpha) = 4/sin² alpha. This is minimised at the largest alpha = pi/4, where sin² alpha = 1/2, giving 8.
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