LIST I (Name of the surface) | LIST II | ||
---|---|---|---|
A. | Ellipsoid | I. x²/a² + y²/b² + z²/c² = 1 | |
B. | Hyperboloid of one sheet | II. x²/a² - y²/b² - z²/c² = 1 | |
C. | Hyperboloid of two sheets | III. -x²/a² + y²/b² + z²/c² = 1 | |
D. | Central conicoid | IV. x²/a² + y²/b² + z = 1 |
The standard equations for the different surfaces are:
Ellipsoid: \( \frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1 \)
Hyperboloid of one sheet: \( \frac{x^2}{a^2} - \frac{y^2}{b^2} - \frac{z^2}{c^2} = 1 \)
Hyperboloid of two sheets: \( -\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1 \)
Central conicoid: \( \frac{x^2}{a^2} + \frac{y^2}{b^2} + z = 1 \)