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JEE Main202118 Mar 2021Morning ShiftMathematicsCircleActual

Choose the correct statement about two circles whose equations are given below: x 2 + y 2 - 10 x - 10 y + 41 = 0 x 2 + y 2 - 22 x - 10 y + 137 = 0

Options

  1. Acircles have same centre
  2. Bcircles have no meeting point
  3. Ccircles have only one meeting point
  4. Dcircles have two meeting points

Correct answer

C. circles have only one meeting point

Step-by-step solution

x 2 + y 2 - 10 x - 10 y + 41 = 0 A ( 5 , 5 ) , R 1 = 3 x 2 + y 2 - 22 x - 10 y + 137 = 0 B ( 11 , 5 ) , R 2 = 3 A B = 6 = R 1 + R 2 Touch each other externally ⇒ circles have only one meeting point.

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