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

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The discussion focuses on finding the equation for a 2-norm of 1 in a 2-dimensional vector space, specifically R^2. The problem requires sketching the root loci for points in R^2 with unity 1-norm, 2-norm, and infinity norm. The user understands how to calculate vector norms but seeks guidance on approaching the sketching aspect of the problem. The equation that points (x,y) must satisfy for a 2-norm of 1 is x² + y² = 1, representing a circle with a radius of 1. This foundational understanding aids in visualizing the different norms in the specified vector space.
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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?
 
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Unity norm means norm 1. What equation must (x,y) satisfy if its 2-norm = 1?
 

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