If the lines joining the origin to the points of intersection of $y=m x+1$ and $x^2+y^2=1$ are perpendicular…
If the lines joining the origin to the points of intersection of $y=m x+1$ and $x^2+y^2=1$ are perpendicular, then .........
$m=-1$ only
$m=1$ only
$m= \pm 1$
$m=0$
Solution
Equation of line joining origin to the points of intersection of $y=m x+1$ and $x^2+y^2=1$ is
$
\begin{array}{rlrl}
x^2+y^2 & =(y-m x)^2 \\
\Rightarrow & & x^2+y^2 & =y^2-2 m x y+m^2 x^2 \\
\Rightarrow & & \left(1-m^2\right) x^2+2 m x y & =0
\end{array}
$
The line are perpendicular if coefficient of $x^2+$ coefficient of $y^2=0$
$
\Rightarrow \quad 1-m^2+0=0 \Rightarrow m= \pm 1
$