Graphing a hyperboloid of one sheet when the right side of the equation is zero

Question

I am attempting to graph a hyperboloid of one sheet. Right now, I am sketching the traces of the hyperboloid in the $(y, z)$ plane. Here is the hyperboloid equation: $$(x-5)^2+(y-5)^2-(z-4)^2 = 1.$$ As you can see, when $4$ is put in place for $x$, this eventually makes the equation of the hyperbola equal to zero. How can this be graphed?

Answer 1

I believe it becomes an Elliptic Cone when it is equal to 0.

Hope this helped