(A) The equation $|z-z_{1}|+|z-z_{2}|=k$ represents an ellipse if $k > |z_{1}-z_{2}|$.In the given equation, $k = 2|z_{1}-z_{2}|$.Since $2|z_{1}-z_{2}

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(A) The equation $|z-z_{1}|+|z-z_{2}|=k$ represents an ellipse if $k > |z_{1}-z_{2}|$.In the given equation, $k = 2|z_{1}-z_{2}|$.Since $2|z_{1}-z_{2}| > |z_{1}-z_{2}|$, the condition for an ellipse is satisfied.Therefore, the locus of $z$ is an ellipse with foci at $z_{1}$ and $z_{2}$.

Class 11 Mathematics 4-1.Complex numbers Geometry of complex numbers

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Let $z_{1}$ and $z_{2}$ be two fixed complex numbers in the Argand plane and $z$ be an arbitrary point satisfying $|z-z_{1}|+|z-z_{2}|=2|z_{1}-z_{2}|$. Then, the locus of $z$ will be

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A
an ellipse
B
a straight line joining $z_{1}$ and $z_{2}$
C
a parabola
D
a bisector of the line segment joining $z_{1}$ and $z_{2}$

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Let $z_{1}$ and $z_{2}$ be two fixed complex numbers in the Argand plane and $z$ be an arbitrary point satisfying $|z-z_{1}|+|z-z_{2}|=2|z_{1}-z_{2}|$. Then, the locus of $z$ will be

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