Question

Match the equation with its graph: -x² y² - z² = 1

1) Circle
2) Ellipsoid
3) Hyperboloid of one sheet
4) Hyperboloid of two sheets

Answer 1

The equation -x² y² - z² = 1 represents a Hyperboloid of one sheet.

Step-by-step explanation:

The equation -x² y² - z² = 1 represents a Hyperboloid of one sheet.

A Hyperboloid of one sheet is a three-dimensional shape that looks like a double cone, where the equation of the surface is defined by the form -(x²/a²) + (y²/b²) - (z²/c²) = 1. In this case, since the x and y terms are squared and the z term is negative, it matches the equation of a Hyperboloid of one sheet.