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AP EAMCET202421 May 2024Evening ShiftMathematicsCircleActual

The equation of the circle touching the circle x^2+y^2-6 x+6 y+17=0 externally and to which the lines x^2-3 x y-3 x+9 y=0 are normal is

Options

  1. Ax^2+y^2-3 x+2 y-2=0
  2. Bx^2+y^2-6 x-2 y+1=0
  3. Cx^2+y^2+6 x-2 y-1=0
  4. Dx^2+y^2-9 x-3 y+2=0

Correct answer

B. x^2+y^2-6 x-2 y+1=0

Step-by-step solution

x^2-3 x y-3 x+9 y=0 (x-3)(x-3 y)=0 x=3, y=1 Centre of required circle =(3,1)r₁+r₂=4 r₁=1 r₂=3 Equation of the required line is aligned & (x-3)^2+(y-1)^2=9 & x^2+y^2-6 x-2 y+1=0 aligned

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