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AP EAMCET202318 May 2023Evening ShiftMathematicsCircleActual

If A and B are the points of intersection of the circles x^2+y^2-4 x+6 y-3=0 and x^2+y^2+2 x-2 y-2=0 then the distance between A and B is

Options

  1. A13 10
  2. B41 3
  3. C231 5
  4. D26 5

Correct answer

C. 231 5

Step-by-step solution

aligned & S₁: x^2+y^2-4 x+6 y-3=0.....(i) & S₂: x^2+y^2+2 x-2 y-2=0.....(ii) aligned aligned & S₁:(x-2)^2+(y+3)^2=4^2 & S₂:(x+1)^2+(y-1)^2=2^2 aligned Here, OA =2, O ^ A =4, O (-1,1) & O ^ (2,-3) OO ^ =5 Let O P=x O^ P=5-x & A P=d In AOP , 2^2= d ^2+ x ^2 .....(1) In APO , 4^2= d ^2+(5- x )^2 .....(2) From eq ^ n (1) & (2) = x = 13 10 , ~d = 231 100 = 231 10 Now, AB =2 AP =2 d =2 231 10 = 231 5

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