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AP EAMCET2009MathematicsCircle

The point (3,-4) lies on both the circles x^2+y^2-2 x+8 y+13=0 and x^2+y^2-4 x+6 y+11=0 . Then, the angle between the circles is

Options

  1. A60^
  2. B⁻¹ ( 1 2 )
  3. C⁻¹ ( 3 5 )
  4. D135^

Correct answer

D. 135^

Step-by-step solution

Given circles are x^2+y^2-2 x+8 y+13=0 and x^2+y^2-4 x+6 y+11=0 . Here, C₁=(1,-4), C₂=(2,-3) , array lll & & r₁= 1+16-13 =2 and & & r₂= 4+9-11 = 2 array Now, d=C₁ C₂= (2-1)^2+(-3+4)^2 = 2 aligned & = d^2-r₁^2-r₂^2 2 r₁ r₂ & = 2-4-2 2 2 2 & =- 1 2 & =135^ aligned

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