(723, #45) Show that if the point (a,b,c) lies on the hyperbolic

(723, #45) Show that if the point (a,b,c) lies on the hyperboloid , then
(a) the line with parametric equations , , lies on this hyperboloid.
(b) the line with parametric equations , , lies on this hyperboloid.
Solution: Note first that since (a,b,c) is on the hyperboloid we have .
Next , if and then

That is, the line lies on the hyperboloid.
An analogous argument is used for part b.