Question

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

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

Answer 1

Answer: (D)

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

Answer 2

((x−2)2+(y−3)2)−((x−3)2−(y−4)2)=1+1
⇒x+y=7