Answer
$\frac{(x-2)^2}{4}+\frac{y^2}{9}=1$
Ellipse: center $(2,0)$, foci $F(2, \pm\sqrt 5)$, vertices $(2, \pm3)$,
major axis length $6$, minor axis length $4$
See graph.
Work Step by Step
Step 1. Make squares of the variables: $9(x^2-4x+4)+4y^2=36$, $9(x-2)^2+4y^2=36$, divide both sides by 36 to get $\frac{(x-2)^2}{4}+\frac{y^2}{9}=1$
Step 2. We can identify that the conic is an ellipse centered at $(2,0)$
Step 3. The major axis is the y-axis, $a=3, b=2, c=\sqrt {3^2-2^2}=\sqrt 5$, the foci are $F(2, \pm\sqrt 5)$
Step 4. The vertices are $(2, \pm3)$,
Step 5. The lengths of the major axis is $2a=6$ and the length of the minor axis is $2b=4$
Step 6. See graph.
