Conic Sections Ellipse

For the given ellipse the measurement for the parameter b, is:

From an equation, the distance among the center of the ellipse and a focus:

The coordinates of the vertex for this ellipse:

The center of the ellipse:
$$\frac{x^2}{25}+\frac{\left(y-3\right)^2}{16}=1$$  

The equation for the ellipse with foci at
  and vertex at is:

$$\frac{x^2}{16}+\frac{\left(y-3\right)^2}{25}=1$$  
The coordinates of the co-vertex of the ellipse:

the center of the ellipse:

Given the equation: $$25x^2\ +\ 100y^2\ -\ 250x\ -600y\ -975=0$$ We can conclude this is a ___________________ ellipse.

Find the standard equation of the given ellipse