Imagine
we slice the bowel z = x2 + y2, called
a paraboloid, with
the vertical plane y =
1.
The cross section becomes a parabola floating
in 3-D space. We can then consider the tangent line to this parabola
at
point (1, 1,
2) that
is contained in the cutting plane.
Note that both the point and the parabola are on the bowel as well.Click
on the graph and an animation will start.