Final answer:
The given equation represents a quadratic surface known as a hyperboloid of two sheets.
Step-by-step explanation:
The given equation represents a quadratic surface in three-dimensional space. The equation of the surface is x² - 2y² - 8z² = 16.
This equation describes a surface that is a hyperboloid of two sheets. It is symmetric about the x-axis and opens upward and downward. The values of x, y, and z satisfy this equation and lie on the surface.
For example, when x = 2, y = 2, and z = 2, the equation is satisfied: 2² - 2(2)² - 8(2)² = 16. Hence, the point (2, 2, 2) lies on the surface.