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JEE Main 2024 Mathematics question

MathematicsParabolaJEE Main 2024

Let A, B and C be three points on the parabola y² = 6x and let the line segment AB meet the line L through C parallel to the x-axis at the point D. Let M and N respectively be the feet of the perpendiculars from A and B on L. Then is equal to .

Answer: 36

Solution

Take A(at₁², 2at₁), B(at₂², 2at₂), C(at₃², 2at₃) with 4a = 6, i.e. a = 3/2. The point D on AB with the same y-coordinate as C is found from the slope of AB; with AM = |2a(t₁

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Question ID VK-016470