First of all, you ask for the center and radius, but you have an ellipse and not a circle. You can talk about a center but not really a radius. If what you want is to know the general shape of what you have, here is what you do.
Start by completing the square for both $X$ and $Y$.
This will give you something of the form
$9(X - H)^2 + 25(Y - K)^2 = S$
Now, divide both sides by $S$ to get something of the form
$\frac{(X - H)^2}{A^2} + \frac{(Y - K)^2}{B^2} = 1$
This is a general form of the equation of an ellipse with center $(H, K)$ (not the most general form, by the way). Then $A$ represents the distance from the center to the edge of the ellipse, if traveling only left or right. And $B$ represents the distance from the center to the edge if traveling up or down. So, the $A$ and $B$ represent something similar to a radius, but not a real radius.