This is an interactive version of a text about quadric surfaces written by Marlene Dieguez Fernandez. The original portuguese document is available here (206 Kb).
You can rotate the objects in the applets below. To do this, click on the object and, keeping the left button pressed, drag the mouse. You can also use the keyboard to temporarily change the operation mode acting over the object: press the key “s” to zoom in/zoom out or the key “t” to translate it and, then, drag the mouse. The key “w” enables auto-rotation the key “r” resets the scene to its initial configuration.
TYPE I: THREE VARIABLES APPEAR |
The equation x^{2}/a^{2} + y^{2}/b^{2} + z^{2}/c^{2} = -1 has no solution for real x, y and z (empty set) and the equation x^{2}/a^{2} + y^{2}/b^{2} + z^{2}/c^{2} = 0 has (0, 0, 0) as its unique solution.
TYPE II: ONLY TWO VARIABLES APPEAR |
The equation x^{2}/a^{2} + y^{2}/b^{2} = -1 has no solution for real x, y and z (empty set) and the solution set of the equation x^{2}/a^{2} + y^{2}/b^{2} = 0 is the z-axis.
TYPE III: ONLY ONE VARIABLE APPEARS |
The equation x^{2}/a^{2} + a^{2} = -1 has no solution for real x, y and z (empty set).