examday

/TMUA

Let $k$ be a positive real constant. For each nonzero real number $m$, define the line $L_m:y=mx+k/m$.

(I) Every line $L_m$ is tangent to the parabola $y^2=4kx$.

(II) For all $m>0$, the lines $L_m$ pass through a common fixed point independent of $m$.

(III) For every $m$, the line $L_{-m}$ is the reflection of $L_m$ in the $y$-axis.

Which of these statements are necessarily true?