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The equation |z-i|+|z+i|=k, k gt 0 can r...

The equation `|z-i|+|z+i|=k, k gt 0` can represent an ellipse, if k=

A

1

B

2

C

4

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We know that the locus of a point P which moves in such a way that the sum of the distances from two fixed points S and `S^(')` is constant, and is greater than `SS^(')`, is an ellipse. So, the locus of P(z), satisfying `|z-i|+|z+i|=k`, will represent an ellipse, if
`k gt` Distance between S(0,1) and `S^(')(0,-1)`
`rArr k gt 2`
Thus, the given equation will represent an ellipse, if k=4.
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