The parabola is defined by these equations:

c(t) = [ 1/param* t^2 , t ]

The caustic of its normals is the cubic y^2 = x^3.

If t1+t2+t3 = 0, then the normals at c(t1), c(t2), c(t3)

all three intersect in one point. Since the parabola

normals are tangents to the caustic, this property of

the caustic tangents is called a "geometric addition".

c(t) = [ 1/param* t^2 , t ]

The caustic of its normals is the cubic y^2 = x^3.

If t1+t2+t3 = 0, then the normals at c(t1), c(t2), c(t3)

all three intersect in one point. Since the parabola

normals are tangents to the caustic, this property of

the caustic tangents is called a "geometric addition".

The construction: Connect the focal point F to an arbitrary point P
on the directrix (yellow line). The symmetry line between

F and P is the tangent of the parabola at a point Q such that PQ is parallel to the axis.

Osculating circles at c(t) are computed using c(t), c'(t), c"(t). They can also be visually identified: The circle is of course

tangential to the curve, but it also passes from one side of the curve to the other (except at the vertex). Watch the demo!

F and P is the tangent of the parabola at a point Q such that PQ is parallel to the axis.

Osculating circles at c(t) are computed using c(t), c'(t), c"(t). They can also be visually identified: The circle is of course

tangential to the curve, but it also passes from one side of the curve to the other (except at the vertex). Watch the demo!