I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 12.4 : Quadric Surfaces
3. Sketch the following quadric surface.
\[z = \frac{{{x^2}}}{4} + \frac{{{y^2}}}{4} - 6\] Show SolutionThis is an elliptic paraboloid that is centered on the \(z\)-axis. Because the \(x\) and \(y\) terms are positive we know that it will open upwards. The “-6” tells us that the surface will start at \(z = - 6\). We can also say that because the coefficients of the \(x\) and \(y\) terms are identical the cross sections of the surface will be circles.
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.
