The Hyperboloid of One Sheet

The Hyperboloid of One Sheet

The intersection of this surface with a horizontal plane z = z₀ is an ellipse. The intersection with a vertical plane x = x₀ or y = y₀ is a hyperbola (Figure 11.1.9).

Figure 11.1.9

The Hyperboloid of Two Sheets

The surface has an upper sheet with z ≥ c and a lower sheet with z < -c. It intersects a horizontal plane z = z₀ in an ellipse if |z₀| > c. It intersects a vertical plane x = x₀ or y = y₀ in a hyperbola (Figure 11.1.10).

Figure 11.1.10