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7.6: Quadric Surfaces

( \newcommand{\kernel}{\mathrm{null}\,}\)

Sketch the trace of the surface $z = x^{2} - y^{2}$ in the plane $x = 1$ .
Sketch the trace of the surface $x^{2} + y^{2} - z^{2} = 1$ in the plane $z = - 2$ .
Sketch the trace of the surface $\frac{z^{2}}{4} - \frac{x^{2}}{9} - \frac{y^{2}}{25} = 1$ in the plane $y = 0$ .
Sketch the trace of the surface $\frac{y^{2}}{16} + \frac{x^{2}}{36} - z^{2} = 1$ in the plane $x = 6$ .
Sketch the surface $y^{2} - x^{2} - z^{2} = 1$ .
Sketch the surface $x^{2} + y^{2} - z^{2} = 4$ .
Sketch the surface $4 x^{2} + y^{2} + 9 z^{2} = 36$ .
Sketch the surface $z = y^{2} - x^{2}$ .
Sketch the surface $4 z = \frac{x^{2}}{4} + y^{2}$ .
Sketch the surface $\frac{y^{2}}{9} + \frac{z^{2}}{4} = x^{2}$ .
Sketch the surface $36 z^{2} - 9 x^{2} - 4 y^{2} = 0$ .
Sketch the surface $\frac{x^{2}}{4} - \frac{z^{2}}{9} - x = 0$ .
Sketch the surface $x = \frac{y^{2}}{16} + \frac{z^{2}}{25}$ .
Sketch the surface $\frac{{(x - 1)}^{2}}{9} + \frac{{(y + 2)}^{2}}{4} + \frac{{(z + 1)}^{2}}{16} = 1$ .
Sketch the surface ${(z - 3)}^{2} - \frac{x^{2}}{25} - \frac{y^{2}}{16} = 1$ .
Sketch the surface $\frac{{(x + 2)}^{2}}{9} + \frac{z^{2}}{4} = 1 + \frac{{(y - 1)}^{2}}{16}$ .