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###### A line of fixed length 2 units moves so that its ends are on the positive $x$-axis and that part of the line $x+y=$ 0 which lies in the second quadrant. The locus of the mid-point of the line has the equation(A) $(x+2 y)^{2}+y^{2}=1$(B) $(x-2 y)^{2}+y^{2}=1$(C) $(x+2 y)^{2}-y^{2}=1$(D) none of these

A line of fixed length 2 units moves so that its ends are on the positive $x$-axis and that part of the line $x+y=$ 0 which lies in the second quadrant. The locus of the mid-point of the line has the equation (A) $(x+2 y)^{2}+y^{2}=1$ (B) $(x-2 y)^{2}+y^{2}=1$ (C) $(x+2 y)^{2}-y^{2}=1$ (D) none of these

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