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AP EAMCET201823 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

S₁: x^2+y^2-2 x+4 y+4=0 Centre, C₁(1,-2) and r₁=1 and S₂: x^2+y^2+4 x-2 y+1=0 Centre C₂(-2,1) and r₂=2 Distance between centres, d is gathered d= (1+2)^2+(-2-1)^2 d= 18 =3 2 d>r₁+r₂ gathered S₁ and S₂ are not intersecting each other. The length of transversal common tangent is aligned & L= d^2- (r₁+r₂ )^2 = (3 2 )^2-9 = 9 & L=3 units aligned

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