Mathematics - Circle Question with Solution | TestHub

The tangent at $(0,1)$ to $x^2+y^2=1$ is the horizontal line $y=1$, so reflection reverses the vertical component of the ray's direction. The reflected ray passes through $(3,1)$ and touches the circle. Tangents from $(3,1)$ to the circle satisfy $|1-3m|/\sqrt{1+m^2}=1$, giving $m=0$ (the mirror line itself, excluded) or $m=3/4$. The reflected ray lies on $y-1=\frac{3}{4}(x-3)$, i.e. $3x-4y-5=0$.