Deforming a Circle

Geometry Level 2

In taxicab geometry, Euclidean distance for a point (x1,y1)(x_1,y_1) and a point (x2,y2)(x_2,y_2) d=(x1x2)2+(y1y2)2d=\sqrt {(x_1-x_2)^2+(y_1-y_2)^2} is replaced by Manhattan distance d=x1x2+y1y2d=|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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