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 $=7+7=14$
