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If z(1) and z(2) are two fixed points in...

If `z_(1) and z_(2)` are two fixed points in the Argand plane, then find the locus of a point z in each of the following
`|z-z_(1)|-|z-z_(2)|=` constant `(ne |z_(1)-z_(2)|)`

A

line passing through A and B

B

line segment joining A and B

C

an ellipse

D

a circle

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`|z-z_(1)|+|z-z_(2)|=|z_(1)-z_(2)|`,
`rArr` PA+ PB=AB
`rArr` P lies on the line segment joining A and B.
`rArr` Locus of P is the line segment joining A and B.
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