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Question

The points of intersection of the line $ax + by = 0,(a \ne b)$ and the circle ${x^2} + {y^2} - 2x = 0$ 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 :

${x^2} + {y^2} + 5x + 5y + 12 = 0$
${x^2} + {y^2} + 3x + 5y + 8 = 0$
${x^2} + {y^2} - 5x - 5y + 12 = 0$
${x^2} + {y^2} + 3x + 3y + 4 = 0$

Solution

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