Answer to Question #75418 in Differential Geometry | Topology for sajid

Question

Q. The hyperboloid of one sheet is S={(x,y,z)∈R^3 |x^2+y^2-z^2=1} show that for every θ,the straight line (x-z)cosθ=(1-y)sinθ,
(x+z)sinθ=(1+y)cosθ
Is contained in S and that every point of hyperboloid lies on one of these deduce that S can be covered by a single surface patch, and hence is a surface.