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AP EAMCET2001MathematicsCircle

The limiting points of the co-axial system containing the two circles aligned & x^2+y^2+2 x-2 y+2=0 and & 25 (x^2+y^2 )-10 x-80 y+65=0 are aligned

Options

  1. A(1,-1),(-3,-40)
  2. B(1,-1), (- 1 5 , 8 5 )
  3. C(-1,1), ( 1 5 , 8 5 )
  4. D(- 1 5 ,- 8 5 )

Correct answer

C. (-1,1), ( 1 5 , 8 5 )

Step-by-step solution

Equation of circles are x^2+y^2+2 x-2 y+2=0 and x^2+y^2- 2 5 x- 16 5 y+ 13 5 =0 aligned & (x^2+y^2+2 x-2 y+2 ) & + [x^2+y^2- 2 5 x- 16 5 y+ 13 5 ]=0 & (1+ ) x^2+(1+ ) y^2+2 (1- 5 ) x & -2 (1+ 8 5 ) y+ (2+ 13 5 )=0 & (1- 5 ) & x^2+y^2+2 1+ 1+ x & - 2 (1+ 8 5 ) 1+ y+ 2+ 13 5 1+ =0 aligned At g=0 1- 5 1+ =0 =5 Then x^2+y^3-3 y+ 5 2 =0 Centre is (0, 3 2 ) . The limiting points are (-1,1), ( 1 5 , 8 5 ) .

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