locus points

**Chris0724** · October 10th 2009, 04:38 AM

The locus of the points (x,y) satisfying the relationship

|z| = 2|z-1|

is

A region exterior to a circle

or

A region interior to a circle

or

A circle

many thanks
ck

**HallsofIvy** · October 10th 2009, 05:22 AM

If z= x+ iy, then $|z|= \sqrt{x^2+ y^2}$ and $|z- 1|= \sqrt{(x- 1)^2+ y^2}$ so your equation says that $\sqrt{x^2+ y^2}= 2\sqrt{(x-1)^2+ y^2}$ . Square both sides of that and reduce. What figure is that?

But with "multiple choice" you should be able to look at that equation and get the answer simply by the fact that it is and equation!

**Chris0724** · October 10th 2009, 06:52 AM

Originally Posted by HallsofIvy

If z= x+ iy, then $|z|= \sqrt{x^2+ y^2}$ and $|z- 1|= \sqrt{(x- 1)^2+ y^2}$ so your equation says that $\sqrt{x^2+ y^2}= 2\sqrt{(x-1)^2+ y^2}$ . Square both sides of that and reduce. What figure is that?

But with "multiple choice" you should be able to look at that equation and get the answer simply by the fact that it is and equation!

hi HallsofIvy,

x^2 + y^2 = constant <--- this is a circle equation...

from the hints you gave, i had achieve the same answer and working but i can't conclude which is the correct answer... is "A circle" wrong ?

**mr fantastic** · October 10th 2009, 02:20 PM

Originally Posted by Chris0724

hi HallsofIvy,

x^2 + y^2 = constant <--- this is a circle equation...

from the hints you gave, i had achieve the same answer and working but i can't conclude which is the correct answer... is "A circle" wrong ?

You found that it's a circle. So why are you having trouble choosing the correct option?!

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