Sketching the solution of an implicit quadratic equation $$G(u,\lambda) = u^2+\lambda^2−9 = 0$$
where $u\in\mathbb{R}$ is the variable of interest and $\lambda\in \mathbb{R}$ is treated as a parameter.
How can I sketch the solution branch for the equation in the plane, and state the points on the branch are isolated?
I tried to used implicit function theorem to prove my solution; however, I still not sure about the second question?

The Pythagorean Theorem jumps out of this equation. It is a circle with a radius of $3.\quad$ Here is the circle inscribed with what has the approximate proportions of the well-known $(3,4,5)$ triangle. In fact, the circle represents an infinite set of right triangles with the hypotenuese $(3)$ having one end on the center and one end on the circle.
