Chapter 9, Problem 7CT

To determine

To graph the ellipse - $x^2+4y^2=16$

Answer to Problem 7CT

The graph is

  

Explanation of Solution

Given:

Equation of Ellipse: $x^2+4y^2=16$

Formula Used:

The standard equation for an ellipse - $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Calculation:

Given:

Equation of Ellipse: $x^2+4y^2=16$

Dividing the above equation by $16$ on both the sides, we have:

  $\begin{array}{l}\frac{x^2+4y^2}{16}=\frac{16}{16}\\ \frac{x^2}{16}+\frac{4y^2}{16}=1\\ \frac{x^2}{16}+\frac{y^2}{4}=1\\ \frac{x^2}{4^2}+\frac{y^2}{2^2}=1\end{array}$

Thus, $a=4$ and $b=2$

Plotting Ellipse on the graph using the above details, we have:

  

Conclusion:

The graph is −