<s>[INST] How to get the center and the axes of an ellipse Get the center and the semimajor/semiminor axes of the following ellipses:
$$x^2-6x+4y^2=16$$
$$2x^2 - 4x+3y^2+6y=7$$
How would one get these? I have no clue. I have a problem with merely rewriting these in the traditional ellipse equation. 
 [/INST] $$x^2-6x+4y^2=16$$
$$(x-3)^2-9+4y^2=16$$
$$(x-3)^2+4y^2=25$$
$$\frac{(x-3)^2}{25}+\frac{4y^2}{25}=1$$
$$\frac{(x-3)^2}{5^2}+\frac{y^2}{(\frac {5}{2})^2}=1$$
center is $O(3,0)$ AND axes are $a=5,b=5/2$, for second ellipse you can proceed similarly
</s>