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Consider the locus of the complex number...

Consider the locus of the complex number `z` in the Argand plane given by `Re(z)-2=|z-7+2i|.` Let `P(z_(1))` and `Q(z_(2))` be two complex numbers satisfying the given locus and also satisfying `arg ((z_(1)-(2+alpha i))/(z_(2)-(2+alpha i)))=(pi)/(2)(alpha in R).` Find the minimum value of `PQ`.[Note: Re(z) denotes real part of complex number `z` and `i^(2)=-1`]

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