Answer
See below
Work Step by Step
Given $9x^2+4y^2-36x-24y+36=0$
We can see that $a=9\\b=0\\c=4$
We will find the discriminant of the given equation $=b^2-4ac\\=0^2-4(9)(4)\\=-144$
Since $-144\lt 0$ and $a\ne c$, the conic is an ellipse.
To graph the ellipse, first complete the square in x.
$9x^2+4y^2-36x-24y+36=0\\9x^2+4y^2-36x-24y=-36\\9(x^2-4x+4)-36+4(y^2-6y+9)-36=-36\\9(x-2)^2+4(y-3)^2=36\\\frac{(x-2)^2}{4}-\frac{(y-3)^2}{9}=1$
From the equation, you can see that the center is at $(2,3)$.
