$\begin{array}{1 1}(A)\;2 \pm \sqrt 2 \\(B)\;-2 \pm \sqrt 2 \\(C)\;-1 \pm \sqrt 2 \\(D)\;none\;of\;these \end{array}$

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Equation of circle $x^2+y^2=1$

$\qquad=(1)^2$

=> $x^2+y^2=(y-mx)^2$

=>$x^2=m^2x^2-2mxy$

=> $x^2(1-m^2)+2mxy=0$

Which represents the pair of lines between which the angle is $45^{\circ}$

$\tan 45=\pm \large\frac{2 \sqrt m^2-0}{1-m^2}$

$\qquad= \large\frac{\pm 2m}{1-m^2}$

=> $1=m^2=\pm 2m$

=> $m^2 \pm 2m-1=0$

=>$m=\large\frac{-2 \pm \sqrt {4+4}}{2}$

$\qquad= \large\frac{-2 \pm 2 \sqrt 2}{2}$

$\qquad= -1 \pm \sqrt 2$

Hence C is the correct answer.

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