JEE Math Practice Question

Let $$\mathrm{z_1=2+3i}$$ and $$\mathrm{z_2=3+4i}$$. The set $$\mathrm{S = \left\{ {z \in \mathbb{C}:{{\left| {z - {z_1}} \right|}^2} - {{\left| {z - {z_2}} \right|}^2} = {{\left| {{z_1} - {z_2}} \right|}^2}} \right\}}$$ represents a

1. A.hyperbola with the length of the transverse axis 7
2. B.hyperbola with eccentricity 2
3. C.straight line with the sum of its intercepts on the coordinate axes equals $$-18$$
4. D.straight line with the sum of its intercepts on the coordinate axes equals $$14$$