JEE Main 2024 Mathematics question
If one of the diameters of the circle x² + y² – 10x + 4y + 13 = 0 is a chord of another circle C, whose center is the point of intersection of the lines 2x + 3y = 12 and 3x – 2y = 5, then the radius of the circle C is :
Answer: (D)
Solution
The given circle has centre O(5, −2) and radius r = √(25 + 4 − 13) = 4. The lines 2x + 3y = 12 and 3x − 2y = 5 meet at (3, 2), the centre of C. The
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