Q53 / 120 · VITEEE 2006 · Mathematics

The region of the argand plane defined by $|z-i|+|z+i| \leq 4$ is

  • A
    interior of an ellipse
  • B
    exterior of a circle
  • Correct answer
    C
    interior and boundary of an ellipse
  • D
    interior of a parabola

Solution

Given, $|z-i|+|z+i| \leq 4$ $\Rightarrow|z-(0+i)|+|z-(0-i)| \leq 0$ This equation represent the interior and boundary of ellipse with foci at $(0,1) \&$ $(0,-1)$, whose major axis is along the $y$-axis.

Hence, the correct answer is option: 'C'.

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