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I'm trying to solve this question I encountered whiles reading a multivariate analysis and i need assistance. An explaination will do. "Define the distance from $ P(x_{1}, x_{2})$ to the origin as $ d(O,P) = max(|x_{1}|,|x_{2}|)$. I'm to plot the locus of points whose squared distance from the origin is $1$. "

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This metric is called the $\ell^{\infty}$ norm. The unit circle is all points $(x,y)$ where $|x| \leq 1$ and $|y| = 1$ or $|y| \leq 1$ and $|x| = 1$. As you can see, this describes a square with vertices $(1,1), (-1,1), (1,-1), (-1,1)$.