Conics.

Considering  only positive values of the weights, for 0 < w < 1 we get an arch of ellipse. For w = 1, we have an arc of parabola, and for w > 1, we have a hyperbola.

The control polygon is the same and the weights for the first and the last point are equal to one.

Can you explain why for w₁=0 the conic is a segment?