Hyperbel als Hüllkuve

R=2;c=4;

v=Sqrt[R^2-u^2]

g[x_,u_]:=u/(c-v) (x-u)+v;
g[x,u]

g[x,u]//Simplify//Factor

gl=D[g[x,u],u]==0//Simplify

lo=Solve[gl,u]

lo[[1,1]]

(((g[x,u]/.lo[[1,1]])//Simplify))//Factor

lox=Solve[gl,x]

xx=lox[[1,1,2]]

yy=g[x,u]/.x->xx//Factor

xx

{ xx,yy}

Eliminate[{xh==xx,yh==yy},{u}]