Coordinate Geometry — Hard JEE math MCQ
**[JEE Mains 2026]** The locus of the point of intersection of tangents drawn to the circle x² + y² = 9 which subtend an angle of 60° at the center is:
- A. x² + y² = 36
- B. x² + y² = 18
- C. x² + y² = 12
- D. x² + y² = 27
Solution
For a circle x² + y² = r² (here r = 3), if tangents from external point P(h, k) subtend angle 2α at center:
tan α = r/d, where d = √(h² + k²) is distance from center to P.
Given 2α = 60°, so α = 30°.
tan 30° = 3/√(h² + k²).
1/√3 = 3/√(h² + k²).
√(h² + k²) = 3√3.
h² + k² = 27.
But tangents subtend angle at center means angle POQ = 60° where O is center, P, Q are points of tangency.
Actually: sin(30°) = r/OP gives OP = 3/sin30° = 6.
Locus: x² + y² = 36.