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AP EAMCET202120 Aug 2021Evening ShiftMathematicsCircleActual

The radical axis of the circles S 1 : x 2 + y 2 - 4 x + 6 y - 10 = 0 and S 2 : x 2 + y 2 + 2 x - 6 y + 2 = 0 cut the circle S 1 in

Options

  1. Atwo real and distinct points
  2. Bone real point
  3. Cimaginary points
  4. Dcan't be determined

Correct answer

A. two real and distinct points

Step-by-step solution

Given: S 1 :   x 2 + y 2 - 4 x + 6 y - 10 = 0 S 2 :   x 2 + y 2 + 2 x - 6 y + 2 = 0 r = g 2 + f 2 - c                     c ≡ - g , - f r 1 = 2 2 + - 3 2 + 10 = 23 c 1 ≡ - g , - f ≡ 2 , - 3 r 2 = - 1 2 + 3 2 - 2 = 1 + 9 - 2 = 8 = 2 2 c 2 ≡ - 1 , 3 c 1 c 2 = 2 + 1 2 + - 3 - 3 2 c 1 c 2 = 9 + 36 c 1 c 2 = 45 c 1 c 2 = 3 5 r 1 + r 2 = 23 + 2 2 Here, c 1 c 2 < r 1 + r 2 So radical axis will cut circles S 1   &   S 2 at

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