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JEE Main 2026 Mathematics question

MathematicsCircleJEE Main 2026

Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines x + (k − 1)y + 3 = 0 and 2x + k²y − 4 = 0. If the line x − y + 2 = 0 intersects the circle at the points A and B, then (AB)² is equal to:

Answer: (C)

Solution

Perpendicularity gives 2 + k²(k − 1) = 0, i.e., k³ − k² + 2 = 0, whose real root is k = −1. This

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Question ID VK-015119