Answer
a. (b)
b. (c)
c. (a)
Work Step by Step
(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).
