What is the equation for a 2-norm of 1 in a 2-dimensional vector?

[JerryG]

Homework Statement

I have a homework problem that asks the following:

Sketch the root locii of points in R^2 having unity 1-norm, 2-norm and infinitynorm.

R^2 is a 2 dimensional vector.

I know how to calculate vector norms, but I'm not sure how to approach the rest of the problem. Can anyone help me out with this problem or point me in the right direction?

 

[LCKurtz]

Unity norm means norm 1. What equation must (x,y) satisfy if its 2-norm = 1?