Obtain the standard formb

$4x^2\+2y^2-z^2-8 x\+4 y\+4 z-2\=0$$\stackrel{\text{manipulate equation}}{\to }$$-\frac{1}{4}{\left(z-2\right)}^2\+\frac{1}{2}{\left(y\+1\right)}^2\+{\left(x-1\right)}^2\=1$

Obtain the equivalent of the surfaces in Figures 3.3.12(a, b)

$4x^2\+2y^2-z^2-8 x\+4 y\+4 z-2\=0$$\to$

Define $f$ so that the graph of $f\=0$ is a quadric surface

$f≔4x^2\+2y^2-z^2-8 x\+4 y\+4 z-2\:$

Complete the square and put $f$ into standard form

$\mathrm{Student}:-\mathrm{Precalculus}:-\mathrm{CompleteSquare}\left(f\=0\,\left[x\,y\,z\right]\right)$

$-\left(-4\right)$

$\frac{4}{}$

Obtain the equivalent of the surfaces drawn in Figures 3.3.12(a, b)

$\mathrm{plots}:-\mathrm{implicitplot3d}\left(f\=0\,x\=-3..5\,y\=-6..4\,z\=-4..8\,\mathrm{scaling}\=\mathrm{constrained}\,\mathrm{axes}\=\mathrm{frame}\,\mathrm{orientation}\=\left[-50\,60\,0\right]\,\mathrm{style}\=\mathrm{surfacecontour}\,\mathrm{tickmarks}\=\left[4\,6\,8\right]\,\mathrm{grid}\=\left[15\,15\,15\right]\right)$