If-z-1-2-z-1-then-the-locus-described-by-the-point-z-in-the-argand-diagram-is-a-

Question Number 19733 by Tinkutara last updated on 15/Aug/17

If ∣ z + 1 ∣ = \sqrt{2} ∣ z - 1 ∣, then the locus

described by the point z in the argand

diagram is a

Answered by ajfour last updated on 15/Aug/17

let z = x + iy

∣ (x + 1) + iy ∣^{2} = 2 ∣ (x - 1) + iy ∣^{2}

\Rightarrow x^{2} + 2 x + 1 + y^{2} = {2 x}^{2} - 4 x + 2 + {2 y}^{2}

or x^{2} - 6 x + y^{2} + 1 = 0

{(x - 3)}^{2} + y^{2} = {(2 \sqrt{2})}^{2}

or ∣ z - 3 ∣= 2 \sqrt{2} .

Commented by Tinkutara last updated on 15/Aug/17

Thank you very much Sir!