JEE Main 2024 Mathematics question
Let the centre of a circle, passing through the point (0, 0), (1, 0) and touching the circle x² + y² = 9, be (h, k). Then for all possible values of the coordinates of the centre (h, k), 4(h² + k²) is equal to ..........
Answer: 9
Solution
A circle through (0, 0) and (1, 0) has its centre on x = 1/2, so h = 1/2, and its equation is x² + y² − 2hx − 2ky = 0 with radius r = √(h² + k²). It touches the circle x² + y² = 9 (centre O) at a point
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