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AP EAMCET201823 Apr 2018Morning ShiftMathematicsCircleActual

If the lengths of the tangents drawn from a point P to the three circles x^2+y^2-4=0 , x^2+y^2-2 x+3 y=0 and x^2+y^2+7 y-18=0 are equal, then the coordinates of P are

Options

  1. A(2, 5)
  2. B(3, 4)
  3. C(4, 3)
  4. D(5, 2)

Correct answer

D. (5, 2)

Step-by-step solution

Radical centre is the locus of point P from which equal length of tangent can be drawn to circle. So, S₁-S₂=0 (x^2+y^2-4 )- (x^2+y^2-2 x+3 y )=0 and S₁-S₃=0 (x^2+y^2-4 )- (x^2+y^2+7 x-18 )=0 -7 y+14=0 gathered 2 x-3(2)-4=0 2 x-6-4=0 2 x=10 x=5 gathered So, radical centre P is (5,2) .

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