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The set of points z satisfying |z+4|+|z-...

The set of points z satisfying `|z+4|+|z-4|=10` is contained or equal to

A

an ellipse with eccentricity `=4/5`

B

the set of points z satisfying `|z| le 3`

C

the set of points z satisfying `|"Re"(z)| le 2`

D

the set of points z satisfying `|"lm"(z)| lt 1`

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`|z+4|+|z-4|=10`
`rArr |z-(4+0i)|+|z-(-4+0i)|=10`
`rArr` Locus of z in an ellipse having foci at `(-4,0)` and (4,0) and major axis equal to 10
`therefore 2a=10` and `2ae=8 rArr e=4/5`
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