Calculus II - Quadric Surfaces

Section 12.4 : Quadric Surfaces

2. Sketch the following quadric surface.

\[\frac{{{x^2}}}{4} + \frac{{{y^2}}}{9} + \frac{{{z^2}}}{6} = 1\]

Show Solution

This is an ellipsoid and because the numbers in the denominators of each of the terms are not the same we know that it won’t be a sphere.

Here are a couple of sketches of the region. We’ve given them with the more traditional axes as well as “boxed” axes to help visualize the surface.

$A three dimensional sketch of the surface $\frac{{{x^2}}}{4} + \frac{{{y^2}}}{9} + \frac{{{z^2}}}{6} = 1$ drawn with the traditional axes. It is an ellipsoid centered at the origin that reaches out 2 units along the x-axis, 3 units along the y-axis and $\sqrt 6 $ units along the z-axis, so it is not quite a sphere.$

$A three dimensional sketch of the same ellipsoid $\frac{{{x^2}}}{4} + \frac{{{y^2}}}{9} + \frac{{{z^2}}}{6} = 1$, this time drawn with “boxed” axes to make the surface easier to visualize.$