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  4. The points of intersection of the line a x+b y=0,(a ≠ b) and the circle x2+y2-2 x=0 are A (α, 0) and B (1, β). The image of the circle with AB as a diameter in the line x+y+2=0 is :

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Q. The points of intersection of the line $a x+b y=0,(a \neq b)$ and the circle $x^2+y^2-2 x=0$ are $A (\alpha, 0)$ and $B (1, \beta)$. The image of the circle with $AB$ as a diameter in the line $x+y+2=0$ is :

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Solution:

Only possibility $\alpha=0, \beta=1$
$\therefore$ equation of circle $x ^2+ y ^2- x - y =0$
Image of circle in $x+y+2=0$ is
$x^2+y^2+5 x+5 y+12=0$