Chapter 8.3, Problem 4P

Solution

To graph: The given equation $0.5x^2+0.5y^2=12$ and verify the graph in a “square window”.

The graph is shown below:

  

Given information:

The given equation is $0.5x^2+0.5y^2=12$

Concept Used:

Step 1: Solve the equation for $y$.

Step 2: Write the two functions as $y_1=$ and $y_2=$.

Step 3: Set the viewing window.

Step 4: Adjust the graph by pressing ZOOM Button and selecting Zsquare.

Calculation:

Solve $0.5x^2+0.5y^2=12$ for $y$.

  $\begin{array}{c}\frac{0.5x^2}{0.5}+\frac{0.5y^2}{0.5}=\frac{12}{0.5}\\ x^2+y^2=24\\ y^2=24-x^2\\ y=\pm \sqrt{24-x^2}\end{array}$

Enter the function $y_1=\sqrt{\left(24-x^2\right)}$ and $y_2=-y_1$ . These functions represent the circle.

Set the viewing window as shown below:

  $\begin{array}{c}{X}_{\min }=-10\\ X_{\max }=10\\ X_{scl}=2\\ Y_{\min }=-10\\ Y_{\max }=10\\ Y_{scl}=2\end{array}$

Adjust the graph by pressing ZOOM Button and selecting Zsquare

The graph is shown below: