Calculus (3rd Edition)

The equation of an ellipsoid is $\left(\frac{x}{a}\right)^{2}+\left(\frac{y}{b}\right)^{2}+\left(\frac{z}{c}\right)^{2}=1$ and to find the trace we freeze one of the three variables for example $z=z_0$, then the equation of the ellipsoid becomes $$\left(\frac{x}{a}\right)^{2}+\left(\frac{y}{b}\right)^{2}=1-\left(\frac{z_0}{c}\right)^{2}$$ which represents an ellipse. However, we can also trace a single point. For example: ($x=0,y=0,z=c$) Thus, not all traces are ellipses.