Sketch the ball $B_2(0,0)$ given a distance function (metric)

Question

For the following question I will denote || || as the $1$-norm on $\mathbb R^2$

i.e. $||(x_1, x_2)|| = |x_1| + |x_2|$.

Let $d: \mathbb R^2 × \mathbb R^2 \rightarrow \mathbb R{^+_0}$ be the distance function with

$$d(x,y) = ||y|| − ||x||$$ if there is $\lambda \in \mathbb R{^+_0}$ so that $x = \lambda y$ or $y = \lambda x$

$$d(x,y) = ||x|| + ||y||$$ If there is no such $\lambda$

By $B_r(p) = x \in X$ $d(x, p) < r$

I set a ball of radius $r$ around a point $p \in X$.

Could anyone explain how I would sketch the ball $B_2(0,0)$. I don't understand how to approach this thanks.