JEE Main 2024 Mathematics question
Consider the circle C : x² + y² = 4 and the parabola P : y² = 8x. If the set of all values of α, for which three chords of the circle C on three distinct lines passing through the point (α, 0) are bisected by the parabola P is the interval (p, q), then (2q − p)² is equal to .
Answer: 80
Solution
Let the midpoint of a chord of the circle be (2t², 4t) on the parabola. The chord (T = S₁) is x(2t²) + y(4t) = 4t⁴ + 16t². Passing through (α, 0): α(2t²) = 4t⁴ + 16t², so α = 2t² + 8. For three
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