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AP EAMCET202318 May 2023Evening ShiftMathematicsCircleActual

If the acute angle between the pair of tangents drawn from the origin to the circle x^2+y^2-4 x-8 y+4=0 is , then =

Options

  1. A3 / 5
  2. B3 / 5
  3. C4 / 3
  4. D4 / 5

Correct answer

C. 4 / 3

Step-by-step solution

aligned & x ^2+ y ^2-4 x -8 y +4=0 & C x ^2+ y ^2 (- g ₁- f )=(2,4) r = 4+16-4 =4 aligned Equation of pair of tangents is S S ₁= T ^2 Where : S : Equation of circle S₁=S(0,0) aligned & & ~T = xx ₁+ y ₁+ g ( x + x ₁ )+ f ( y + y ₁ )+ c =0 & ( x ^2+ y ^2-4 x -8 y +4 )(0+4)=( x 0+ y 0-2( x -0) & -4( y -0)+4)^2 & 4 ( x ^2+ y ^2-4 x -8 y +4 )=(-2 x -4 y +4)^2 & 12 y ^2+16 xy =0 aligned Tangent of acute angle between pairs of straight line a x^2+2 b x y+b y^2 is = 2 (h^2-a b ) a+b In equation (i) a=0, b=12, h=8 = 2 (8^2-

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