$z_1, z_2$ are two complex numbers with $\left|z_1-z_2\right| < k$. If the complex number $z$ satisfies the…
$z_1, z_2$ are two complex numbers with $\left|z_1-z_2\right| < k$. If the complex number $z$ satisfies the condition $\left|z-z_1\right|+\left|z-z_2\right|=k$, then $z$ lies on
a parabola
an ellipse
a circle
a hyperbola
Solution
According to the given information,
$
\left|z-z_1\right|+\left|z-z_2\right|=K>\left|z_1-z_2\right|
$
$\Rightarrow$ Sum of the distances of the point $z$ from $z_1$ and $z_2$ is constant $(K)$ and more than the distance between points $z_1$ and $z_2$.
So, locus of point ' $z$ ' is an ellipse.
Hence, option (b) is correct