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The circle C x^2+y^2+kx+(1-k)y+(k+1)=0 p...

The circle C `x^2+y^2+kx+(1-k)y+(k+1)=0` passes through two fixed points for every real number k Find (i)the coordinates of these two points (ii) minimum value of the radius of circle C

Text Solution

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`x^2+y^2+y-1+k(x+y-1)=0`
`S_!+lambdaC_1=0`
`(1-y)^2+y^2+y-1=0`
`1-2y+y^2+y^2+y-1=0`
`2y^2-y=0`
`y(2y-1)=0`
`y=0,x=1`
`y=1/2,y=1/2`
...
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