Chapter 13 - Vector Geometry - 13.6 A Survey of Quadratic Surfaces - Exercises - Page 693: 40

$$\left(\frac{x}{2}\right)^{2}+\left(\frac{y}{4}\right)^{2}=1.$$

By observing Figure 15(B), we get that $$ a=2, \quad b=4.$$ Plugging into the equation on page 692, we get: $$\left(\frac{x}{2}\right)^{2}+\left(\frac{y}{4}\right)^{2}=1.$$