If `|z+3i|+|z-i|=8`, then the locus of z, in the Argand plane, is

Options

A. an ellipse of eccentricity `1/2` and major axis along x-axis.
B. an ellipse of eccentricity `1/2` and major axis of along y-axis.
C. an ellipse of eccentricity `1/sqrt(2)` and major axis along y-axis
D. none of these

Answer

A

Explanation

We have,
`|z+3i|+|z-i|=8`
`rArr SP + S^(')P=8`, where `S^(')(0,-3),S(0,1)` and `P(z)` are points in the Argand plane.
`rArr` Locus of P is an ellipse having foci at `S^(')` and S and major axis=8.
`therefore 2b=8` and `2be = S^(')S=4`
`rArr` b=4 and be=2 `rArr e=1/2`