JEE Main 2024 Mathematics question
Let P(α, β) be a point on the parabola y² = 4x. If P also lies on the chord of the parabola x² = 8y whose mid-point is (1, 5/4). Then (α – 28)(β – 8) is equal to .
Answer: 192
Solution
P lies on y² = 4x, so β² = 4α. The chord of x² = 8y with midpoint (1, 5/4) is T = S₁: x − 4(y + 5/4) = 1 − 10, i.e. x − 4y + 4 = 0. Substituting α = 4β − 4 into β² = 4α gives β² − 16β +
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