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AP EAMCET2008MathematicsComplex 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

  1. Acircle
  2. Bpair of lines
  3. Cparabola
  4. 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.

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