## Calculus (3rd Edition)

(a) The equation can be written in the form $$\left(\frac{x}{4}\right)^{2}+\left(\frac{y}{2}\right)^{2}+\left(\frac{z}{2}\right)^{2}=1$$ Hence it intersects the $x,y,z$ axes at $(\pm 4,0,0),(0,\pm 2,0), (0,0,\pm 2)$. Thus, this ellipsiod is the figure (b). (b) The equation can be written in the form $$\left(\frac{x}{2}\right)^{2}+\left(\frac{y}{4}\right)^{2}+\left(\frac{z}{2}\right)^{2}=1$$ Hence it intersects the $x,y,z$ axes at $(\pm 2,0,0),(0,\pm 4,0), (0,0,\pm 2)$. Thus, this ellipsiod is the figure (c). (c) The equation can be written in the form $$\left(\frac{x}{2}\right)^{2}+\left(\frac{y}{2}\right)^{2}+\left(\frac{z}{4}\right)^{2}=1$$ Hence it intersects the $x,y,z$ axes at $(\pm 2,0,0),(0,\pm 2,0), (0,0,\pm 4)$. Thus, this ellipsiod is the figure (a).