Let $z _ { 1 } = 2 + 3 i$ and $z _ { 2 } = 3 + 4 i$. The set $\mathrm { S } = \left\{ \mathrm { z } \in \mathrm { C } : \left| \mathrm { z } - \mathrm { z } _ { 1 } \right| ^ { 2 } - \left| \mathrm { z } - \mathrm { z } _ { 2 } \right| ^ { 2 } = \left| \mathrm { z } _ { 1 } - \mathrm { z } _ { 2 } \right| ^ { 2 } \right\}$ represents a (1) straight line with sum of its intercepts on the coordinate axes equals 14 (2) hyperbola with the length of the transverse axis 7 (3) straight line with the sum of its intercepts on the coordinate axes equals $-18$ (4) hyperbola with eccentricity 2
Let $z _ { 1 } = 2 + 3 i$ and $z _ { 2 } = 3 + 4 i$. The set $\mathrm { S } = \left\{ \mathrm { z } \in \mathrm { C } : \left| \mathrm { z } - \mathrm { z } _ { 1 } \right| ^ { 2 } - \left| \mathrm { z } - \mathrm { z } _ { 2 } \right| ^ { 2 } = \left| \mathrm { z } _ { 1 } - \mathrm { z } _ { 2 } \right| ^ { 2 } \right\}$ represents a\\
(1) straight line with sum of its intercepts on the coordinate axes equals 14\\
(2) hyperbola with the length of the transverse axis 7\\
(3) straight line with the sum of its intercepts on the coordinate axes equals $-18$\\
(4) hyperbola with eccentricity 2