Let $ u=\frac{2 z+i}{z-k i}, \mathrm{z}=x+i y $ and $ k0 $. If the curve represented by $ \operatorname{Re}(u)+\operatorname{Im}(u)=1 $ intersects the $ y $-axis at the point $ P $ and $ Q $ where $ P Q=5 $, then the value of $ k$ is [JEE Main 2020, 4 Sep (Shift 1)]

Question

Let $ u=\frac{2 z+i}{z-k i}, \mathrm{z}=x+i y $ and $ k>0 $. If the curve represented by $ \operatorname{Re}(u)+\operatorname{Im}(u)=1 $ intersects the $ y $-axis at the point $ P $ and $ Q $ where $ P Q=5 $, then the value of $ k$ is [JEE Main 2020, 4 Sep (Shift 1)]

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Let \( u=\frac{2 z+i}{z-k i}, \mathrm{z}=x+i y \) and \( k>0 \). If the curve represented by \( \operatorname{Re}(u)+…

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