JEE Main202325 Jan 2023Morning ShiftMathematicsComplex NumberActual
Let z 1 = 2 + 3 i and z 2 = 3 + 4 i . The set S = z ∈ C : z - z 1 2 - z - z 2 2 = z 1 - z 2 2 represents a
Options
- Astraight line with sum of its intercepts on the coordinate axes equals 14
- Bhyperbola with the length of the transverse axis 7
- Cstraight line with the sum of its intercepts on the coordinate axes equals - 18
- Dhyperbola with eccentricity 2
Correct answer
A. straight line with sum of its intercepts on the coordinate axes equals 14
Step-by-step solution
Given, z 1 = 2 + 3 i and z 2 = 3 + 4 i and the set S = z ∈ C : z - z 1 2 - z - z 2 2 = z 1 - z 2 2 , Now putting the value of z = x + i y ,   z 1 = 2 + 3 i and z 2 = 3 + 4 i in z - z 1 2 - z - z 2 2 = z 1 - z 2 2 we get, ⇒ ( x - 2 ) 2 + ( y - 3 ) 2 - ( x - 3 ) 2 - ( y - 4 ) 2 = 1 + 1 ⇒       x + y = 7 Which is a straight line with intercept 7 on x   &   y axis, so sum of intercept will be 7 + 7 = 14 .