Mathematics - Circle Question with Solution | TestHub

Equation of circles $x^2+y^2=1=(1{)}^2$ $$\begin{array}{rl}& \Rightarrow x^2+y^2=(y-mx{)}^2\Rightarrow x^2=m^2{x}^2-2mxy\Rightarrow x^2\left(1-m^2\right)+2mxy=0\\ & \tan 45=\pm \frac{2\sqrt{m^2-0}}{1-m^2}=\frac{\pm 2m}{1-m^2}\Rightarrow 1-m^2=\pm 2m\Rightarrow m^2\pm 2m-1=0\\ & \Rightarrow m=\frac{-2\pm \sqrt{4+4}}{2}=\frac{-2\pm 2\sqrt{2}}{2}=-1\pm \sqrt{2}\end{array}$$