Question

Use a graphing device to graph theellipse.

$6x^2+y^2=36$

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,

$\begin{array}{l}\Rightarrow a^2=6\\ \Rightarrow a=\sqrt{6}\\ \Rightarrow b^2=36\\ \Rightarrow b=6\\ \Rightarrow c=\sqrt{36-6}\\ \Rightarrow c=\sqrt{30}\\ \Rightarrow c=5.5\end{array}$

Hence,

The coordinates of the vertices are $\left(\pm 2.4,0\right)$

The coordinates of the foci are $\left(0,\pm 5.5\right)$