# locus points

• Oct 10th 2009, 04:38 AM
Chris0724
locus points
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
• Oct 10th 2009, 05:22 AM
HallsofIvy
If z= x+ iy, then $\displaystyle |z|= \sqrt{x^2+ y^2}$ and $\displaystyle |z- 1|= \sqrt{(x- 1)^2+ y^2}$ so your equation says that $\displaystyle \sqrt{x^2+ y^2}= 2\sqrt{(x-1)^2+ y^2}$. 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!
• Oct 10th 2009, 06:52 AM
Chris0724
Quote:

Originally Posted by HallsofIvy
If z= x+ iy, then $\displaystyle |z|= \sqrt{x^2+ y^2}$ and $\displaystyle |z- 1|= \sqrt{(x- 1)^2+ y^2}$ so your equation says that $\displaystyle \sqrt{x^2+ y^2}= 2\sqrt{(x-1)^2+ y^2}$. 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 ? (Wondering)
• Oct 10th 2009, 02:20 PM
mr fantastic
Quote:

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 ? (Wondering)

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