### Complex Number Question 3

#### Question 3 - 25 January - Shift 1

Let $z_1=2+3 i$ and $z_2=3+4 i$. The set

$S={z \in C:|z-z_1|^{2}-|z-z_2|^{2}=|z_1-z_2|^{2}}$

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

## Show Answer

#### Answer: (1)

#### Solution:

#### Formula: Equation of a line

$((x-2)^{2}+(y-3)^{2})-((x-3)^{2}-(y-4)^{2})=1+1$

$\Rightarrow x+y=7$

Now, intercept form of the given line is $\frac{x}{7}+\frac{y}{7} = 1$

Intercept on $x-$ axis = $7$ and

Intercept on $y-$ axis $7$

sum of intercepts $=7+7=14$