Geometry Coordinate

nekteo

1. The problem statement, all variables and given/known data
Given that Z is a complex number with condition |Z-1|+|Z+1|=7

Illustrate Z on Argand Diagram and write out the equation of Locuz Z


I attempted to figured out the equation of locus Z,
|Z-1|+|Z+1|=7
|x+yi-1|+|x+yi+1|=7
[tex]\sqrt{}[(x-1)^2+y^2][/tex] + [tex]\sqrt{}[(x+1)^2 + y^2][/tex] = 7
[tex]\sqr{}x^2 + 1 - 2x + y^2 + x^2 + 1 + 2x + y^2 = 49[/tex]
[tex]\sqr{}2x^2 + 2y^2 = 47[/tex]

it's not necessary the correct answer though...
however, I can't figure how to illustrate the diagram! help!

genneth

Assuming that your calculations are correct, that gives a circle of radius [tex]\sqrt{47/2}[/tex]. However, I don't think it is... Check your algebra carefully -- squaring both sides doesn't mean get rid of square roots!

Another way to think about it is that the original equation says that the distance from a point on the locus to the points +1 and -1 add up to 7. This is the condition for an ellipse with its foci at -1 and 1! And an ellipse is only a circle if the foci coincide.