Chapter 9.7, Problem 17WE

To determine

To graph:

The following inequality equations:

  $\begin{array}{l}{x}^2+4y^2\le 16\\ x^2\le y^2+4\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}{x}^2+4y^2\le 16\\ x^2\le y^2+4\end{array}$

Graph:

  

Interpretation:

The given inequality equation rewrite as:

  $x^2+4y^2\le 16$  ... (1)

It is the ellipse equation.

And

  $x^2\le y^2+4$

Subtract $y^2$ from both sides of equation:

  $x^2-y^2\le y^2-y^2+4$

  $x^2-y^2\le 4$  ... (2)

It is hyperbola equation.

The graph of eq. (1) and (2) is shown above by using the Desmos graphing calculator.