Question
Let PQ and MN be two straight lines touching the circle x^ 2 +y^ 2 -4 x-6 y-3=0 at the points A and B respectively. Let O be the centre of the circle and AOB = / 3. Then the locus of the point of intersection of the lines PQ and MN is :
JEE Main
Mathematics
Circle
2026
JEE Main 2026 (21 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. x^ 2 +y^ 2 -12 x-18 y-25=0
- B. 3 (x^ 2 +y^ 2 )-18 x-12 y+25=0
- C. 3 (x^ 2 +y^ 2 )-12 x-18 y-25=0
- D. x^ 2 +y^ 2 -18 x-12 y-25=0
Answer
C. 3 (x^ 2 +y^ 2 )-12 x-18 y-25=0
Step-by-step solution
Circle: (x-2)^2 + (y-3)^2 = 16, center O = (2, 3), radius r = 4. For tangents from external point P touching at A and B with AOB = /3: In quadrilateral OAPB: APB = - /3 = 2 /3, so OPA = /3. In right triangle OAP: ( /3) = 4 OP . OP = 8 3 = 8 3 3 . Locus: (x-2)^2 + (y-3)^2 = 64 3 . 3(x^2 + y^2) - 12x - 18y - 25 = 0.
Related: Mathematics — Circle · All PYQ Banks