Chapter 1, Problem 8P

To determine

To find: The graph for the given equation.

Explanation of Solution

Given:

The given equation is $x^4-4x^2-x^2{y}^2+4y^2=0$ .

Calculation:

Consider the given equation is,

  $x^4-4x^2-x^2{y}^2+4y^2=0$

Then,

  $\begin{array}{l}{x}^4-4x^2-x^2{y}^2+4y^2=0\\ x^2\left(x^2-4\right)\left(x^2-y^2\right)=0\\ \left(x-2\right)\left(x+2\right)\left(x-y\right)\left(x+y\right)=0\end{array}$

Then, the zeroes of the above equation are,

  $\begin{array}{l}y=-x\\ y=x\\ x=-2\\ x=2\end{array}$

The graph for the equation is shown in Figure 1

  

Figure 1