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AP EAMCET2010MathematicsCircle

If the circle x^2+y^2+2 x+3 y+1=0 cuts another circle x^2+y^2+4 x+3 y+2=0 in A and B , then the equation of the circle with A B as a diameter is

Options

  1. Ax^2+y^2+x+3 y+3=0
  2. B2 x^2+2 y^2+2 x+6 y+1=0
  3. Cx^2+y^2+x+6 y+1=0
  4. D2 x^2+2 y^2+x+3 y+1=0

Correct answer

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

Step-by-step solution

The equation of the circles are S₁ x^2+y^2+2 x+3 y+1=0 and S₂ x^2+y^2+4 x+3 y+2=0 Since, the circles cuts each other at A and B then equation of A B is S₁-S₂=0 (x^2+y^2+2 x+3 y+1 ) - (x^2+y^2+4 x+3 y+2 )=0 -2 x-1=0 x= -1 2 Putting the value x=- 1 2 in S₂ , we get 1 4 +y^2-2+3 y+2=0 4 y^2+12 y+1=0 y= -12 144-16 8 y= -12 128 8 = -12 8 2 8 y= -3 2 2 So intersection points are A (- 1 2 ,- 3 2 + 2 ) and (- 1 2 ,- 3 2 - 2 ) . Then equation of circle with diameter A B is (x+ 1 2 ) (x+ 1 2 )+ (y+ 3 2 + 2 ) (y+ 3 2 - 2 )=0

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