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AP EAMCET202022 Sep 2020Evening ShiftMathematicsCircleActual

If the length of the tangent from (f, g) to the circle x^2+y^2=6 be twice the length of the tangent from the same point to the circle x^2+y^2+3 x+3 y=0 , then f^2+g^2+4 f+4 g+2 is equal to

Options

  1. A–1
  2. B1
  3. C0
  4. D–2

Correct answer

C. 0

Step-by-step solution

aligned & Given, P=(f, g) & S: x^2+y^2-6=0 & S^ : x^2+y^2+3 x+3 y=0 aligned According to the question, S₁₁ =2 S₁₁^ Squaring on both sides ( S₁₁ )^2= (2 S₁₁^ )^2 gathered S₁₁=4 S₁₁^ (g^2+f^2-6 )=4 (g^2+f^2+3 g+3 f ) 3 g^2+3 f^2+12 g+12 f+6=0 gathered Dividing by 3 on both sides, g^2+f^2+4 g+4 f+2=0 Hence, option (3) is correct.

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