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JEE Main 2024 Mathematics question

MathematicsParabolaJEE Main 2024

Let a line perpendicular to the line 2x − y = 10 touch the parabola y² = 4(x − 9) at the point P. The distance of the point P from the centre of the circle x² + y² − 14x − 8y + 56 = 0 is .

Answer: 10

Solution

A line perpendicular to 2x − y = 10 has slope −1/2. For y² = 4(x − 9) with point (9 + t², 2t) the slope is

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Question ID VK-011666