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

Step-by-step solution

Given that x^2+(x+1)^2+x+1-1=0 [from Eq. (i)] array lc & 2 x^2+3 x+1=0 & (2 x+1)(x+1)=0 & x=- 1 2 ,-1 and y= 1 2 , 0 array Point of A (- 1 2 , 1 2 ) and B(-1,0) These are the end points of a diameter. The equation of circle is (x+ 1 2 )(x+1)+ (y- 1 2 )(y-0)=0 array rrrl & (2 x+1)(x+1)+(2 y-1) y=0 & 2 x^2+x+2 x+1+2 y^2-y=0 & 2 (x^2+y^2 )+3 x-y+1=0 array