The window "Domain" displays a domain as a wireframe, a point (u0, v0) 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 Xu(u0,v0) and Xv(u0,v0) to the surface at the point X(u0,v0), and the normal vector Xu(u0,v0) × Xv(u0,v0) to the surface at the point X(u0,v0).

Checking the "Show tangent plane" checkbox will show the tangent plane to X(u,v) at the point X(u0,v0). (Note that this box is checked by default.) It is possible to change u0, v0, a, b, and c in the control window.