JEE Main 2024 Mathematics question
Let a circle passing through (2, 0) have its centre at the point (h, k). Let , be the point of intersection of the lines 3x + 5y = 1 and (2 + c)x + 5c²y = 1. If h = and k = , then the equation of the circle is :
Answer: (A)
Solution
Solving the two lines, = (1 − c²)/(2 + c − 3c²) and = (c − 1)/(5(2 + c − 3c²)). As c → 1: h = lim (1 − c)(1 + c)/((1 − c)(2 + 3c)) = 2/5 and k = lim (c − 1)/(−5(c − 1)(3c + 2)) = −1/25. The
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