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COMEDK2023Morning ShiftMathematicsCircleActual

The points of intersection of circles (x+1)^2+y^2=4 and (x-1)^2+y^2=9 are (a, b) , then (a, b) equals to

Options

  1. A(-1,2)
  2. B(1,3)
  3. C(1.25, 3 4 7 )
  4. D(-1.25, 3 4 7 )

Correct answer

D. (-1.25, 3 4 7 )

Step-by-step solution

The given equations of the circles are: (x+1)^2 + y^2 = 4 (1) (x-1)^2 + y^2 = 9 (2) Expanding both equations: x^2 + 2x + 1 + y^2 = 4 x^2 + y^2 + 2x = 3 (3) x^2 - 2x + 1 + y^2 = 9 x^2 + y^2 - 2x = 8 (4) Subtracting equation (4) from equation (3): (x^2 + y^2 + 2x) - (x^2 + y^2 - 2x) = 3 - 8 4x = -5 x = -1.25 Substituting x = -1.25 into equation (3): (-1.25)^2 + y^2 + 2(-1.25) = 3 1.5625 + y^2 - 2.5 = 3 y^2 - 0.9375 = 3 y^2 = 3.9375 y^2 = 39375 10000 = 63 16 y = 63 16 = 3 7 4 Thus, the points of intersection are (-1.2

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