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

JEE Advanced Mathematics question

The equation , , can represent an ellipse if is

(A)1
(B)2
(C)4Correct
(D)none of these

Answer: (C)

Solution

says the sum of distances of from the fixed points and is . This is an ellipse with foci iff exceeds the distance between the foci, . ( gives only the segment joining and ; gives no point.) Among the options only works.

Book's algebraic rou

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Question ID VK-108111