The equation of the tangent line at the point parameter λ = 1 to the curve r = (1 + λ, -λ2, 1 + λ3) is:

If the tangential and normal accelerations of a particle describing a plane curve are constant throughout, then the radius of curvature ρ at any point is given by (where a and b are arbitrary constants, and t is time):

The envelope of the family of straight lines y = mx + √(a2m2 + b2), where a, b are constants and m is the parameter, represents: