Deforming a Circle

Geometry Level 2

In taxicab geometry, Euclidean distance for a point \((x_1,y_1)\) and a point \((x_2,y_2)\) \[d=\sqrt {(x_1-x_2)^2+(y_1-y_2)^2}\] is replaced by Manhattan distance \[d=|x_1-x_2|+|y_1-y_2|\] and the shape of circles may change as well.

What is the shape of taxicab circles?

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