Let z1=2+3 i and z2=3+4 i. The set S= z ∈ C:|z-z1|2-|z-z2|2=|z1-z2|2 represents a

Question

Let z1=2+3 i and z2=3+4 i. The set S= z ∈ C:|z-z1|2-|z-z2|2=|z1-z2|2 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

Tardigrade Admin · Accepted Answer

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

Q. 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

straight line with the sum of its intercepts on the coordinate axes equals $- 18$

hyperbola with eccentricity 2

hyperbola with the length of the transverse axis 7

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

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

Q. Let z1​=2+3i and z2​=3+4i. The set S={z∈C:∣z−z1​∣2−∣z−z2​∣2=∣z1​−z2​∣2} represents a

straight line with the sum of its intercepts on the coordinate axes equals −18