Answer
Six quadric surfaces are :
1)Ellipsoid$$(\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1)$$
2)Hyperboloid of one sheet$$(\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1)$$
3)Hyperboloid of two sheets$$(-\frac{x^2}{a^2}-\frac{y^2}{b^2}+\frac{z^2}{c^2}=1)$$
4)Elliptic Cone$$(\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=0)$$
5)Elliptic Paraboloid$$(z=\frac{x^2}{a^2}+\frac{y^2}{b^2})$$
6)Hyperbolic Paraboloid$$(z=-\frac{x^2}{a^2}+\frac{y^2}{b^2})$$
Work Step by Step
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