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MathsJEE Main 21 Jan 2026, Shift 1·Q15·MCQ·Moderate

Circles · Locus from tangents to circle

Let PQPQ and MNMN be two straight lines touching the circle x2+y2−4x−6y−3=0x^2 + y^2 - 4x - 6y - 3 = 0 at the points AA and BB respectively. Let OO be the centre of the circle and ∠AOB=π/3\angle AOB = \pi/3. Then the locus of the point of intersection of the lines PQPQ and MNMN is:
  1. (1)3(x2+y2)−18x−12y+25=03(x^2 + y^2) - 18x - 12y + 25 = 0
  2. (2)x2+y2−12x−18y−25=0x^2 + y^2 - 12x - 18y - 25 = 0
  3. (3)x2+y2−18x−12y−25=0x^2 + y^2 - 18x - 12y - 25 = 0
  4. (4)3(x2+y2)−12x−18y−25=03(x^2 + y^2) - 12x - 18y - 25 = 0

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See the full 21 Jan 2026, Shift 1 paper