# Geometry Coordinate

by nekteo
Tags: coordinate, geometry
 P: 9 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 $$\sqrt{}[(x-1)^2+y^2]$$ + $$\sqrt{}[(x+1)^2 + y^2]$$ = 7 $$\sqr{}x^2 + 1 - 2x + y^2 + x^2 + 1 + 2x + y^2 = 49$$ $$\sqr{}2x^2 + 2y^2 = 47$$ it's not necessary the correct answer though... however, I can't figure how to illustrate the diagram! help!
 P: 980 Assuming that your calculations are correct, that gives a circle of radius $$\sqrt{47/2}$$. 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.