If the chord $y=mx+1$ of the circle $x^2+y^2=1$ subtends an angle of measure ${45}^0$ at the major segment of the circle then m = 
 

$$\begin{gathered} \mathrm{Given} \mathrm{chord} \mathrm{y}=\mathrm{mx}+1 \\ \Rightarrow \mathrm{y}-\mathrm{mx}=1\to \left(1\right) \\ Given circle {\mathrm{x}}^2+{\mathrm{y}}^2-1=0\to \left(2\right) \\ homogeni\sin g \left(2\right) with help of \left(1\right) then \\ {\mathrm{x}}^2+{\mathrm{y}}^2-1{(y-mx)}^2=0 coeff x^2+coeff of y^2=0 \\ \Rightarrow 1+1-1-m^2=0 \\ \Rightarrow m^2=1 \\ \Rightarrow m=\pm 1 \end{gathered}$$

Angle major segment is 135

M=tan135=-1