If x-y+1=0 meets thwe cicle `x^(2)+y^(2)+y-1=0`at a and b, then the equation of the circle with ab as diameter, is

Options

A. `2(x^(2)+y^(2))+3x-y+1=0`
B. `2(x^(2)+y^(2))+3x-y+2=0`
C. `2(x^(2)+y^(2))+3x-y+3=0`
D. `2(x^(2)+y^(2)+3x-y+1=0`

Answer

A

Explanation

The intersection points of line and circle are aA `(-1/2,1/2)` and B(-1,0).
` these are then end points of a dimeter. `
` :. The equation of cricle is `(x+1/2)(x+1)+(y-1/2)(y-0)=0`
`rArr(2x+1)(x+1)+(2y-1)y=0`
`rArr r^(2)(x^(2)+y^(2))+3x-y=1=0`