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Consider the locus of the complex number z in the Argand plane is given by Re (z)-2=|z-7+2 i| . Let P (z₁ ) and Q (z₂ ) be two complex number satisfying the given locus and also satisfying ( z₁-(2+ i) z₂-(2+ i) )= 2 ( R) then the minimum value of P Q is divisible by

Options

  1. A3
  2. B5
  3. C7
  4. D2

Correct answer

D. 2

Step-by-step solution

aligned & z=x+i y & (x-2)^2=(x-7)^2+(y+2)^2 & (x-2)^2-(x-7)^2=(y+2)^2 aligned aligned & (y+2)^2=5(2 x-9) & (y+2)^2=10 (x- 9 2 ) & Y^2=4 a X a= 5 2 & .P Q |_ =L(L R)=10 aligned

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