Consider the equation below.

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y$^\{2\}=$x$^\{2\}+6$ z$^\{2\}+6$

$\backslash ]$

Reduce the equation to one of the standard forms.

Classify the surface.

ellipsoid

elliptic paraboloid

hyperbolic paraboloid

cone

hyperboloid of one sheet

hyperboloid of two sheets

Sketch the surface. $($If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.$)$

$($Write an equation for the cross section at $\backslash ($ z$=0\backslash )$ using $\backslash ($ x $\backslash )$ and $\backslash ($ y $\backslash ).)$

$($Write an equation for the cross section at $\backslash ($ y$=-4\backslash )$ using $\backslash ($ x $\backslash )$ and $\backslash ($ z $\backslash ).)$

$($Write an equation for the cross section at $\backslash ($ y$=0\backslash )$ using $\backslash ($ x $\backslash )$ and $\backslash ($ z $\backslash ).)$

$($Write an equation for the cross section at $\backslash ($ y$=4\backslash )$ using $\backslash ($ x $\backslash )$ and $\backslash ($ z $\backslash ).)$

$($Write an equation for the cross section at $\backslash ($ x$=0\backslash )$ using $\backslash ($ y $\backslash )$ and $\backslash ($ z $\backslash ).)$