For k = 2

The polar coordinate is employed here to represent the support point. That is

(x₁, x₂)=()

where is the radial distance from the design origin, and θ is the counterclockwise angle from the x₁ axis.

The model matrix:

The h₂(r) is an increasing function for r > 0. Then the maximum of |X’X| is attended when r = 2 and θ=0.

Hence the original star points are the D-optimal star points.