Chapter 10.7, Problem 37AYU

In Problems 35-38, find parametric equations that define the curve shown.

To determine

To find: A parametric equation for the curves defined.

Answer to Problem 37AYU

$x=3\text{cos}t$ and $y=2\text{sin}t$, $0\le t\le 2\pi$

Explanation of Solution

Given:

Calculation:

From the graph we see $x$ and $y$ intercepts as $\left(-3,0\right),\left(3,0\right),(0,2)$ and $\left(0,-2\right)$.

Let $x=3\text{cos}t$ and $y=2\text{sin}t$ such that $0\le t\le 2\pi$.

The parametric equation is,

$x=3\text{cos}t$ and $y=2\text{sin}t$, $0\le t\le 2\pi$