Complex NumbersHard
Question
The equation ||z + i| - |z - i|| = k represents
Options
A.a hyperbola if 0 < k < 2
B.a pair of ray if k > 2
C.a straight line if k = 0
D.a pair of ray if k = 2
Solution
||z + i| - |z - i|| = k
for 0 < k < 2 its hyperbola having foci as i & - i.
for k = 0 |z + i| = |z - i| which is perpendicular bisector of line joining i, - i
for k = 2 a pair of ray.
for 0 < k < 2 its hyperbola having foci as i & - i.
for k = 0 |z + i| = |z - i| which is perpendicular bisector of line joining i, - i
for k = 2 a pair of ray.
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