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Find the range of K for which the equati...

Find the range of `K` for which the equation `|z+i| - |z-i | = K` represents a hyperbola.

A

`k in (-2,2)`

B

`k in [2,2]`

C

`k in (0,2)`

D

`k in (-2,0)`

Text Solution

Verified by Experts

The correct Answer is:
A
We know that the locus of a point P is a hyperbola if it moves in such a way that the absolute value of the differences of its distances from two fixed points S and `S^(')` (say) is constant, and is less than than `SS^(')`
So, the given equation will represent a hyperbola, if
`|k| lt` Distance between S(0,1) and `S^(')(0,-1)`
`rArr |k| lt 2 rArr k in (-2,2)`.
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