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AP EAMCET2005MathematicsCircle

The equation of the circle whose diameter is the common chord of the circles x^2+y^2+2 x+3 y+2=0 and x^2+y^2+2 x-3 y-4=0 is

Options

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

Correct answer

C. x^2+y^2+2 x+2 y+1=0

Step-by-step solution

Given that Equation of common chord is aligned S₁-S₂ & =0 6 y+6=0 y & =-1 aligned Putting y=-1 in Eq. (i), we get array rlrl & & & x^2+1+2 x-3+2=0 & & x^2+2 x=0 x=0,-2 array End points of diameter are (0,-1) and (-2,-1) Equation of circle is aligned (x-0) & (x+2)+(y+1)(y+1) & =0 & x^2+2 x+y^2+2 y+1 & =0 aligned

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