Let u =(2 z+i)/(z- k i), z=x+i y and k >0. If the curve represented by Re ( u )+ Im ( u )=1 intersects the y -axis at the points P and Q where PQ =5,…

Let $\displaystyle \mathrm{u}=\frac{2 z+i}{z-\mathrm{k} i}, z=x+i y$ and $\displaystyle \mathrm{k}>0$. If the curve represented by $\displaystyle \operatorname{Re}(\mathrm{u})+\operatorname{Im}(\mathrm{u})=1$ intersects the $\displaystyle y$-axis at the points P and Q where $\displaystyle \mathrm{PQ}=5$, then the value of k is :