Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.6 Parametric Equations, Graphs, and Applications - 8.6 Exercises - Page 400: 51

$x = a~cos~t$ $y = b~sin~t$ $t$ in $[0,2\pi]$

$cos^2~t+sin^2~t = 1$ $\frac{a^2~cos^2~t}{a^2}+\frac{b^2~sin^2~t}{b^2} = 1$ $\frac{(a~cos~t)^2}{a^2}+\frac{(b~sin~t)^2}{b^2} = 1$ Let $~~x = a~cos~t$ Let $~~y = b~sin~t$ $\frac{x^2}{a^2}+\frac{y^2}{b^2} = 1$ Therefore, this is a parametric representation of the original equation: $x = a~cos~t$ $y = b~sin~t$ $t$ in $[0,2\pi]$