Here we see the definition of the 
Minkowski distance from an 
arbitrary point (x, y) to the origin.

For p=2, we have the Euclidean distance. 
For p=1, we have the taxicab distance. 

Varying p, we see how the shape 
of the circle evolves in each case.

$\textsf{\LARGE O}$

p = 2 (slider from 0.5 to 3, step 0.25)
r: 4
ec1:=(abs(x))^(p) + (abs(y))^(p) = r^(p)
O: (0, 0)
l1 = Sequence((abs(x))^(k) + (abs(y))^(k) = r^(k), k, 0.5, 3, 0.1)
texto2: "XO(x, y)=(|x|^p+|y|^p)^{1/p}\\
=" + (LaTeX[LaTeX[If[p ≟ 1, "", "("]]]) + "" + (LaTeX[If[p ≟ 2, "x", "|x|"]]) + "^{" + (LaTeX[If[p ≟ 1, "", ("" * p)]]) + "}+" + (LaTeX[If[p ≟ 2, "y", "|y|"]]) + "^{" + (LaTeX[If[p ≟ 1, "", ("" * p)]]) + "}" + (LaTeX[If[p ≟ 1, "", ")"]]) + "^{" + (LaTeX[If[p ≟ 1, "", ("1/" * p)]]) + "}"