There are two types of equations for ellipses



where the ellipse looks like the cross section of an egg
resting on a table.

and



where the ellipse is upright like the number zero "0".

In either case a is half the major axis and b is half the minor axis.

The major axis is always larger than the minor axis.  So a > b.

In the case where  a = b, the ellipse is a circle.

The center is the point (h,k).  The foci are two points 

inside the ellipse on the major axis which are c units from the 

center, where c is gotten from the equation .

Your ellipse



is the type that is upright like the letter zero "0", because the
larger denominator is under the term in y.  So we compare it to



and we see that h=-5, k=7,  so  and 

So the center is (-5,7), the major axis is 2*5 or 10 and the minor
axis is 2*7=14, so we draw the graph:



We draw in the major and minor axes, which cross at the center:



The foci are on the major axis and are c units above and
below the center.  We calculate c







So the foci are 4 units directly above and below the center (-5,7).

One focus is at (-5,11) and the other is at (-5,3)




You didn't ask for the vertices and the co-vertices.

They are at the ends of the major and minor axes.

The vertices are (-5,2) and (-5,12)
The covertices are at (-8,7) and (-2,7)

Edwin