The equation $|z - 5i| / |z + 5i| = 12,$ where $z = x + iy,$ represents a/an

If the center of a regular hexagon is at the origin and one of the vertices on the Argand diagram is $1 + 2i$,then its perimeter is

If $z_{1}$ and $z_{2}$ are two non-zero complex numbers such that $\frac{z_{1}}{z_{2}}+\frac{z_{2}}{z_{1}}=1$, then the origin and the points represented by $z_{1}$ and $z_{2}$:

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

The points $z_1, z_2, z_3, z_4$ in the complex plane are the vertices of a parallelogram taken in order,if and only if

The points in the set $\{z \in \mathbb{C} : \arg \left(\frac{z-2}{z-6i}\right) = \frac{\pi}{2}\}$ (where $\mathbb{C}$ denotes the set of all complex numbers) lie on the curve which is a