Parametric equations and interception with parabola

What kind of sheaf of lines does the parametric equation represent?

It represents a sheaf of lines passing through a point ...........................................

What happens 1<k<5?

The sheaf of lines...............................................

What happens for k=1 and k=5

The sheaf of lines..........................................................

What happens for k<1 or k>5?

The sheaf of lines......................................................