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

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

how does |z-z_(1)|+|z-z_(2)|=k represents ellipse

Find the range of K for which the equation |z+i| - |z-i | = K represents a hyperbola.

The equation |z+i|-|z-i|=k represents a hyperbola, if

Find the range of K for which the equation |z+i|-|z-i|=K represents a hyperbola.

If |z-z_(1)|-|z-z_(2)||=k, where k<|z_(1)-z_(2)| represents a hyperbola in argand plane then the equation of the asymptotes of the hyperbola are

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

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

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