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AP EAMCET202119 Aug 2021Morning ShiftMathematicsCircleActual

The radius of the circle whose centre lies at ( 1 , 2 ) , while cutting the circle x 2 + y 2 + 4 x + 16 y - 30 = 0 orthogonally, in units.

Options

  1. A41
  2. B31
  3. C21
  4. D11

Correct answer

D. 11

Step-by-step solution

Given circle equation is x 2 + y 2 + 4 x + 16 y - 30 = 0 By comparing with x 2 + y 2 + 2 g x + 2 f y + c = 0 2 g = 4 ,   2 f =   16   &   c = - 30 Centre =   C 1   =   - g ,   - f   =   - 2 ,   - 8 Radius =   r 1   =   g 2 + f 2 - c   =   4 + 64 + 30 =   98 Other circle centre C 2   =   1 ,   2 Distance between centres =   d   = C 1 C 2   =   - 3 2 + 10 2 = 109 We know that when two circles ar

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