The equation |z+i|-|z-i|=k represents a hyperbola if

JEE Advanced Mathematics question

The equation represents a hyperbola if

(A)Correct
(B)
(C)
(D)none of these

Answer: (A)

Solution

: the difference of distances from the foci and is constant. A difference of distances is at most the focal distance , and for the locus is a branch of the hyperbola with foci (the upper branch for , the lower for ).

Following the method of Q77 (valid for ,

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Question ID VK-108112