Let ${\mathrm{z}}_1=2+3\mathrm{i}$  and ${\mathrm{z}}_2=3+4\mathrm{i}$  . The set $\mathrm{S}=\{\mathrm{z}\in \mathrm{ℂ}:{|\mathrm{z}-{\mathrm{z}}_1|}^2-{|\mathrm{z}-{\mathrm{z}}_2|}^2={|{\mathrm{z}}_1-{\mathrm{z}}_2|}^2\}$  represents a
 

hyperbola with the length of the transverse axis 7

Straight line with the sum of its intercepts on the coordinate axes equals -18 

Straight line with the sum of its intercepts on the coordinate axes equals 14 

hyperbola with eccentricity 2