JEE Main 2024 Mathematics question
Let C : x² + y² = 4 and C′ : x² + y² − 4λx + 9 = 0 be two circles. If the set of all values of λ so that the circles C and C′ intersect at two distinct points, is R − [a, b], then the point (8a + 12, 16b − 20) lies on the curve:
Answer: (D)
Solution
Centre distance 2|λ| and radius √(4λ² − 9): two intersection points iff |λ| > 13/8, so a = −13/8, b = 13/8 and the point is (−1, 6).