Answer
see graph
Work Step by Step
Dividing both sides by 36, then the standard form of the equation $
4x^2+9y^2=36
$ is
\begin{array}{l}
\dfrac{x^2}{9}+\dfrac{y^2}{4}=1
.\end{array}
This is the equation of the ellipse with the following properties:
\begin{array}{l}
\text{Center: }(0,0)
,\\\text{Major axis parallel to: }x-\text{axis}
,\\\text{$a$ = }3
,\\\text{Vertices: }(-3,0), (3,0)
,\\\text{$b$ = }2
,\\\text{Co-vertices: }(0,-2), (0,2)
.\end{array}
Using the properties above, the graph of the given equation is shown below.
