Chapter 11.3, Problem 5QR

To determine

To find: The use of the calculator in function mode to graph the curve $x^2+3y^2=4$ .

Answer to Problem 5QR

After solving the graph $y=\sqrt{\frac{4-x^2}{3}}$ and $y=-\sqrt{\frac{4-x^2}{3}}$ the entire curve will be obtained.

Explanation of Solution

Given information:

Expression of the curve $x^2+3y^2=4$ .

Calculation:

Given that theexpression of the curve is $x^2+3y^2=4$ .

Simplify the expression and solve for $y$ .

  $\begin{array}{c}{x}^2+3y^2=4\\ 3y^2=4-x^2\\ y^2=\frac{4-x^2}{3}\\ y=\pm \sqrt{\frac{4-x^2}{3}}\end{array}$

Conclusion:

Hence, after solving the graph $y=\sqrt{\frac{4-x^2}{3}}$ and $y=-\sqrt{\frac{4-x^2}{3}}$ the entire curve will be obtained.