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AP EAMCET2007MathematicsComplex Number

The locus of the point z=x+i y satisfying | z-2 i z+2 i |=1 is

Options

  1. Ax -axis
  2. By -axis
  3. Cy=2
  4. Dx=2

Correct answer

A. x -axis

Step-by-step solution

aligned & Given, | z-2 i z+2 i |=1 & |x+i y-2 i| |x+i y+2 i| =1 aligned aligned & x^2+(y-2)^2 = x^2+(y+2)^2 & x^2+y^2+4-4 y=x^2+y^2+4+4 y & 8 y=0 & y=0 ie, x -axis. & aligned

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