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AP EAMCET2015MathematicsCircle

If x-y+1=0 meets the circle x^2+y^2+y-1=0 at A and B , then the equation of the circle with A B as diameter is

Options

  1. A2 (x^2+y^2 )+3 x-y+1=0
  2. B2 (x^2+y^2 )+3 x-y+2=0
  3. C2 (x^2+y^2 )+3 x-y+3=0
  4. Dx^2+y^2+3 x-y+4=0

Correct answer

A. 2 (x^2+y^2 )+3 x-y+1=0

Step-by-step solution

Given that circle, S=x^2+y^2+y-1=0 Line, L : x-y+1=0 Equation of the circle passing through the intersection of line and circle is given by aligned & S + L =0 & (x^2+y^2+y-1 )+ (x-y+1)=0 & x^2+y^2+ x+(1- ) y+ -1=0 aligned Centre of above circle = ( - 2 , -1 2 ) Since, centre lies on x-y+1=0 - 2 - ( -1 2 )+1=0 = 3 2 Now, the required equation of circle aligned & x^2+y^2+y-1+ 3 2 (x-y+1)=0 & 2 (x^2+y^2 )+3 x-y+1=0 aligned

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