I'm in need of some help to address this problem.
Let $C$ be a curve given by two equations:
$x^2+y^2-z^2-1=0$,
$x^2-y^2-z^2-1=0$
Express the curve by means of parametric equations.
Any ideas on how to work on it?
differential-geometryparametricparametrization
I'm in need of some help to address this problem.
Let $C$ be a curve given by two equations:
$x^2+y^2-z^2-1=0$,
$x^2-y^2-z^2-1=0$
Express the curve by means of parametric equations.
Any ideas on how to work on it?
Best Answer
Subtract the two equations. We get $y=0$
Plug in the first $$x^2-z^2=1$$ A parametrization is $$(x=\cosh t,y=0,z=\sinh t); (x=-\cosh t , y=0, z=-\sinh t)$$ In the image below the two surfaces and their intersection.
$$...$$