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: (B)

$ \left(( x -2)^2+( y -3)^2\right)-\left(( x -3)^2-( y -4)^2\right)=1+1 $
$\Rightarrow x + y =7$