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(C) The equation of the pair of lines joining the origin to the points of intersection of the line $y=mx+1$ and the circle $x^2+y^2=1$ is obtained by

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$m=\pm 1$

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(C) The equation of the pair of lines joining the origin to the points of intersection of the line $y=mx+1$ and the circle $x^2+y^2=1$ is obtained by homogenizing the circle equation using the line equation $y-mx=1$.Substituting $1 = y-mx$ into $x^2+y^2=1^2$,we get:$x^2+y^2=(y-mx)^2$$x^2+y^2=y^2-2mxy+m^2x^2$$(1-m^2)x^2+2mxy=0$For these lines to be perpendicular,the sum of the coefficients of $x^2$ and $y^2$ must be zero.Here,the coefficient of $x^2$ is $(1-m^2)$ and the coefficient of $y^2$ is $0$.Therefore,$(1-m^2)+0=0$$1-m^2=0$$m^2=1$$m=\pm 1$

If the lines joining the origin to the points of intersection of $y=mx+1$ and $x^2+y^2=1$ are perpendicular,then .........

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