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Section 12.4 : Quadric Surfaces

Sketch each of the following quadric surfaces.

1. \(\displaystyle {z^2} = {x^2} + \frac{{{y^2}}}{2}\)
2. \(z = 2 + 4{x^2} + 6{y^2}\)
3. \(4{x^2} + {y^2} + 3{z^2} = 1\)
4. \(\displaystyle \frac{{{x^2}}}{9} + \frac{{{y^2}}}{{16}} = 1\)
5. \(\displaystyle y = \frac{{{x^2}}}{2} + \frac{{{z^2}}}{3} - 7\)
6. \(6{x^2} + 2{z^2} = 1\)
7. \(\displaystyle x = 12 - \frac{{{y^2}}}{4} - 3{z^2}\)
8. \({x^2} = 4{y^2} + 9{z^2}\)