Math Insight

Applet: Elliptic paraboloid cross sections

The elliptic paraboloid $z = x^2 + y^2$ is plotted on a square domain \begin{gather*} -2 \le x \le 2\\ -2 \le y \le 2 \end{gather*} in the first panel and on the circular domain determined by $z \le 8$ in the second panel. You can drag the blue points on the sliders to change the location of the different types of cross sections.

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