The hyperboloid ($=0$) is the result of rotating $4 y^2 = 1 + x^2$ around the $x$-axis. So, carefully draw $4 y^2 = 1 + x^2$ in the $x,y$ plane.
– Will JagyMar 12 '13 at 18:11
@Beyonce90: Is this what you are looking for? It is plotted as a parametric plot using WA. Also, do you see how following Will Jagy's advice would have solved the problem?
– AmzotiMar 12 '13 at 19:45