how does `|z-z_1|+|z-z_2| =k` represents ellipse

How does |z-z1|-|z-z2||=K represents hyperbola

If the equation |z-z_1|^2 + |z-z_2|^2 =k , represents the equation of a circle, where z_1 = 3i, z_2 = 4+3i are the extremities of a diameter, then the value of k is

If the equation |z-z_1|^2 + |z-z_2|^2 =k , represents the equation of a circle, where z_1 = 3i, z_2 = 4+3i are the extremities of a diameter, then the value of k is

The least possible integral value of k for which |z-1-i|+|z+i|=k represents an ellipse is

Prove that |z-z_1|^2+|z-z_2|^2 = k will represent a circle if |z_1-z_2|^2 le 2k.

Prove that |z-z_1|^2+|z-z_2|^2=k will represent a real circle with center ((z_1+z_2)/2) on the Argand plane if 2kgeq|z_1-z_2|^2

If the equation |z-z_(1)|^(2)+|z-z_(2)|^(2)=k represents the equation of a circle,where z_(1)=2+3 iota,z_(2)=4+3t are the extremities of a diameter,then the value of k is

If k gt 0, k ne 1, and z_(1), z_(2) in C , then |(z-z_(1))/(z-z_(2))| = k represents

The equation |z-i|+|z+i|=k, k gt 0 can represent an ellipse, if k=

The equation |z-i|+|z+i|=k, k gt 0 can represent an ellipse, if k=