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please anyone, how to solve this ????

For a circle centered at \[z_0=a+bi\] with radius C the condition must be
\[\left|z-z_0\right|=C^2\]

what is value of Z here ...... its ans is " option a" but how to solve this ??

\[z=x+iy \rightarrow |z|=\sqrt{x^2+y^2}\]this is what you use to solve this.

\[|z+4|=|(x+iy)+4|=|(x+4)+iy|=\sqrt{(x+4)^2+y^2}\]Similarly with the second magnitude.

|z+4| is the distance of all z from (-4,0)
and |z-4| is the distance of all z from (4,0)

as the sum of distances from two fixed points is 10, a constant, thus it is an ellipse

in case of hyperbola, we take the diffence from two fixed points

difference*

ok

you're welcome

Pretty much. Your finding the locus of points that satisfy the condition you're given.

np probs. good luck with it :)