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AP EAMCET20228 Jul 2022Evening ShiftMathematicsComplex NumberActual

If |z-3 i|+|z+5 i|=4 , then the locus of z is

Options

  1. ANo such point z exists.
  2. BEllipse
  3. CParabola
  4. DCircle

Correct answer

A. No such point z exists.

Step-by-step solution

Given, |z-3 i|+|z+5 i|=4 It is of the form |z-z₁ |+ |z-z₂ |=k (i) Eq. (i) represents an ellipse if k> |z₁-z₂ | Here, z₁=3 i and z₂=-5 i aligned & |z₁-z₂ |=|3 i+5 i|=|8 i|=8 and k=4 & But k < |z₁-z₂ | aligned Hence, no such point z exists.

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