\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{25}} = \frac{{{z^2}}}{{36}},\,\,\,{\text{is }}\,{\text{the equation }}\,{\text{of _____}}{\text{.}}

• A) paraboloid
• B) cylinder
• C) cone
• D) sphere

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• A) Only the x-axis
• B) None
• C) Only the xy-plane
• D) All coordinate planes and the origin

{\text{Trace}}\,\,{\text{of}}\,\,{\text{a cone}}\,\,\,{x^2} + \,\,\frac{{{y^2}}}{9} = {z^2},\,\,\,{\text{in}}\,\,xz - {\text{plane}}\,\,\,{\text{is }}\_\_\_\_\_.

• A) y = \pm \,3\,z
• B) x = \pm \,\,\frac{y}{3}
• C) no trace
• D) x = \pm \,\,z

\frac{{{x^2}}}{9} + \frac{{{y^2}}}{{16}} + \frac{{{z^2}}}{{16}} = 1,\,\,\,{\text{is }}\,{\text{the equation }}\,{\text{of _____}}{\text{.}}

• A) ellipsoid
• B) cone
• C) paraboloid
• D) hyperboloid

{\text{When}}\,\,a = b = c,\,\,\,{\text{the}}\,\,{\text{ellipsoid}}\,\,\,\,\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} = 1,\,\,\,{\text{becomes}}\,\,{\text{the}}\,\_\_\_\_\_.

• A) cone
• B) paraboloid
• C) hyperboloid
• D) sphere

\[\frac{{{x^2}}}{9} + \frac{{{y^2}}}{{16}} + \frac{{{z^2}}}{{16}} = 1,\,\,\,{\text{is }}\,{\text{the equation }}\,{\text{of _____}}{\text{.}}\]

• A) ellipsoid
• B) hyperboloid
• C) cone
• D) paraboloid

\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{25}} = z, is an equation of ______.

• A) Elliptic paraboloid
• B) Hyperboloid of two sheets
• C) Hyperboloid of one sheet
• D) Hyperbolic paraboloid