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AP EAMCET202315 May 2023Morning ShiftMathematicsCircleActual

If the coordinates of point, of contact of the circles x ^2+ y ^2-4 x +8 y +4=0 and x ^2+ y ^2+2 x =0 is ( a , b ) , then a+2 b=

Options

  1. A-1
  2. B-2
  3. C0
  4. D1

Correct answer

B. -2

Step-by-step solution

Circle x^2+y^2-4 x+8 y+4=0 have centre P(2,-4) and radius 4 unit and circle x^2+y^2+2 x=0 have centre Q(-1,0) and radius 1 unit Let O(a, b) be the point of contact. aligned & O(a, b)= 4(-1)+1(2) 4+1 , 4(0)+1(-4) 4+1 & = (- 2 5 ,- 4 5 ) & a+2 b=-2 aligned

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