Distance between a point $x\in\mathbb R^n$ and $x_1^2+x_2^2\le 4$

by Annelise t.   Last Updated January 16, 2018 06:20 AM

Let $S=\{(x_1,x_2):x_1^2+x_2^2\le 4\}$. Let $f(y)=inf\{||y-x||:x\in S\}$. Find $f$ explicitly.

Attempt:

This is the $f(y)$ I got so far

$$inf\{\sqrt{(y_1-x_1)^2+(y_2-x_2)^2}:(x_1+x_2)\in S\}$$

How do I relate $f(y)$ with $x_1^2+x_2^2\le 4\}$?



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