Question
Let a circle of radius 4 pass through the origin O, the points A (- 3 a, 0) and B (0,- 2 b), where a and b are real parameters and a b 0. Then the locus of the centroid of O A B is a circle of radius
JEE Main
Mathematics
Circle
2026
JEE Main 2026 (24 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 7 3 3
- B. 8 3
- C. 11 3
- D. 5 3
Answer
B. 8 3
Step-by-step solution
Circle of radius 4 passes through O and points A(- 3a , 0), B(0, - 2b ). Let center be C(h, k) on circle: h^2 + k^2 = 16. Since A, B lie on circle: 3a^2 + 2 3a h + h^2 + k^2 = 16 gives h = - 3a 2 And h^2 + 2b + 2 2b k + k^2 = 16 gives k = - 2b 2 Centroid G = ( - 3a 3 , - 2b 3 ). Setting x = - 3a 3 and y = - 2b 3 : a = 3x^2 and b = 9y^2 2 From h^2 + k^2 = 16: 3a 4 + 2b 4 = 16 → 3a + 2b = 64 Substituting: 9x^2 + 9y^2 = 64 → x^2 + y^2 = 64 9 Radius = 8 3
Related: Mathematics — Circle · All PYQ Banks