Question

Use a graphing device to graph theellipse.

$x^2+2y^2=8$

Short answer

Hence, the graph of the ellipse is as shown:

Step-by-step solution

Step 1. Given information.

Given the equation of ellipse .

substitution method.

Step 2. Write down the concept.

Comparing the given equation with the standard equation,

$\begin{array}{l}\Rightarrow a^2=8\\ \Rightarrow a=\sqrt{8}\\ \Rightarrow b^2=4\\ \Rightarrow b=2\\ \Rightarrow c=\sqrt{{\left(\sqrt{8}\right)}^2-2^2}\\ \Rightarrow c=\sqrt{8-4}\\ \Rightarrow c=2\end{array}$

Hence,

The coordinates of the vertices are $\left(\pm 2.83,0\right)$

The coordinates of the foci are $\left(\pm 2,0\right)$