Hyperboloid of One Sheet; Finding equation for lines contained in it.

[coocoo]

Hello,

I would love help with the following proof:

Let S be the standard hyperboloid of one sheet: (x^2)+(y^2)-(z^2)=1.
Let P=(a,b,0) be a point with ((a^2)+b^2))=1; therefore P is in the intersection of S with the xy-plane.

Prove that there are exactly two lines through the point P that lie entirely on the surface of S.

Thank you!

 

[mmm4444bot]

These boards are for tutoring. Please explain what you've considered thus far. Cheers :cool:

 

[HallsofIvy]

It is difficult to "help" if we don't know what you have done and where you have difficulty.

I will say this- do you know the general parametric equations for a line in three dimensions? Put those equations for x, y, and z into the equation of the hyperbola and see what has to be true in order that every point on the line satisfy the equation.