How do the x-y, x-z, and y-z planes divide three-dimensional space?

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Diagram showing a double cone intersected by planes at different angles, producing the conic sections: a horizontal plane creates a circle, a tilted plane creates an ellipse, a plane parallel to the cone's side forms a parabola, and a steep plane produces a hyperbola. Each section is labeled, with the axis and apex of the cone indicated. — analytic geometry The conic sections result from intersecting a plane with a double cone, as shown in the figure. There are three distinct families of conic sections: the ellipse (including the circle), the parabola (with one branch), and the hyperbola (with two branches).

In analytic geometry, the three-dimensional Cartesian coordinate system utilizes three perpendicular axes—the x-, y-, and z-axes—which intersect at the origin.

These axes define three primary coordinate planes: the x-y plane, the y-z plane, and the x-z plane. By intersecting one another at right angles, these three planes partition three-dimensional space into eight distinct regions known as octants.1