It can also produce ellipsoids, spheres, cones, and cylinders but you should use the sphere , cone , and cylinder objects built into POV-Ray because they are faster than the quadric version. A quadric is a 2nd order polynomial while a quartic is 4th order.
Quadrics render much faster and are less error-prone but produce less complex objects.
Although the syntax actually will parse 3 vector expressions followed by a float, we traditionally have written the syntax as above where A through J are float expressions. J will give different shapes. If you take any three dimensional point and use its x, y and z coordinates in the above equation the answer will be 0 if the point is on the surface of the object. The answer will be negative if the point is inside the object and positive if the point is outside the object. The easiest way to use these shapes is to include the standard file shapes.inc into your program.