z_1 and z_2 are two complex numbers such that | vedclass

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(B) The given equation is $\left|z-z_1\right|+\left|z-z_2\right|=k$. This represents the locus of a point $z$ such that the sum of its distances from

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an ellipse

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(B) The given equation is $\left|z-z_1\right|+\left|z-z_2\right|=k$. This represents the locus of a point $z$ such that the sum of its distances from two fixed points $z_1$ and $z_2$ is a constant $k$. Since the condition $\left|z_1-z_2\right| By the definition of an ellipse,the locus of a point whose distance from two fixed points (foci) has a constant sum is an ellipse. Therefore,$z$ lies on an ellipse. Thus,option $(B)$ is correct.

$z_1$ and $z_2$ are two complex numbers such that $\left|z_1-z_2\right| < k$. If a complex number $z$ satisfies the condition $\left|z-z_1\right|+\left|z-z_2\right|=k$,then $z$ lies on:

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