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AP EAMCET201825 Apr 2018Morning ShiftMathematicsCircleActual

The length of the transverse common tangent of the circles x 2 + y 2 - 2 x + 4 y + 4 = 0 and x 2 + y 2 + 4 x - 2 y + 1 = 0 is

Options

  1. A3
  2. B17
  3. C15
  4. D3

Correct answer

D. 3

Step-by-step solution

Let, C 1 ≡ x 2 + y 2 - 2 x + 4 y + 4 = 0 Centre, c 2 ≡ 1 , - 2 and radius r 1 = 1 C 2 ≡ x 2 + y 2 + 4 x - 2 y + 1 = 0 Centre, c 1 ≡ - 2 , 1 and radius r 2 = 2 Now, distance between centres is given by c 1 c 2 = - 2 - 1 2 + 1 + 2 2 = 18 Now, we know that the length of transverse common tangent is given by c 1 c 2 2 - r 1 + r 2 2 = 18 - 1 + 2 2 = 3 .

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