Highly selective Backlog Qs for JEE MainMathematicsComplex Number
The points in the set z C: ( z-2 z-6 i )= 2 (where C denotes the set of all complex numbers) lie on the curve which is a
Options
- Acircle
- Bpair of lines
- Cparabola
- Dhyperbola
Correct answer
A. circle
Step-by-step solution
Given that, ( z-2 z-6 i )= 2 (z-2)- (z-6 i)= 2 Let z=x+i y aligned & [(x-2)+i y]- [x+i(y-6)]= 2 & ⁻¹ y x-2 - ⁻¹ y-6 x = 2 & ( y x-2 - y-6 x 1+ y x-2 y-6 x )= 2 & 1+ y x-2 y-6 x =0 & x(x-2)+y(y-6)=0 aligned This is an equation of circle in diametric form.