The window "Domain" displays a domain as a
wireframe, a point (u_{0}, v_{0}) in the domain, and
the u-constant and
v-constant curves
through that point in red and green, respectively.

The "Surface X(u,v)" window shows the hyperboloid of one sheet X(u,v) =
(a*cos(u)cosh(v), b*sin(u)cosh(v), c*sinh(v)) for
the
given domain, the images of the point and the curves from the
"Domain" window, the tangent vectors X_{u}(u_{0},v_{0})
and X_{v}(u_{0},v_{0}) to the
surface at the point X(u_{0},v_{0}), and the normal
vector X_{u}(u_{0},v_{0}) × X_{v}(u_{0},v_{0})
to the
surface at the point X(u_{0},v_{0}).

Checking the "Show
tangent plane" checkbox will show the tangent plane to X(u,v) at the
point
X(u_{0},v_{0}). (Note that this box is checked by
default.) It is possible to change u_{0}, v_{0}, a, b,
and c in the control window.