The equation of tangent to the circle $x^2+y^2=1$, which is perpendicular to the line $y=m x+1$; is
The equation of tangent to the circle $x^2+y^2=1$, which is perpendicular to the line $y=m x+1$; is
$x+m y-\sqrt{1+m^2}=0$
$m x+y-\sqrt{1+m^2}=0$
$x+m y+\sqrt{1+m^2}=0$
$m x+y+\sqrt{1+m^2}=0$
Solution
The equation of tangent to the circle
$
x^2+y^2=1 \text { is } y=m_1 x+\sqrt{1+m_1^2}
$
The line is perpendicular to the line $y=m x+1$
$
\begin{aligned}
& y=\frac{-1}{m} x+\sqrt{1+\frac{1}{m^2}} \\
\Rightarrow & m y=-x+\sqrt{m^2+1} \\
\Rightarrow \quad & x+m y-\sqrt{m^2+1}=0
\end{aligned}
$