Question 74290
Find the center, vertices and foci of the following ellipse:

(x + 3)^2/9 + (y + 1)^2/16 =1
:
The equation for an ellipse whose denominator is largest under the y's is:
{{{highlight((x-h)^2/b^2+(y-k)^2/a^2=1)}}}
Characteristics:
a>b and {{{b^2=a^2-c^2}}}
Major axis is parallel to the y-axis.
Center:(h,k)
Foci: (h,k+c), (h,k-c)
Vertices: (h,k+a), (h,k-a)
:
Your equation has:
h=-3
k=-1
a^2=16--->a=4
b^2=9---->b=3
{{{b^2=a^2-c^2}}}
{{{b^2-a^2=-c^2}}}
{{{-b^2+a^2=c^2}}}
{{{-9+16=c^2}}}
{{{7=c^2}}}
{{{sqrt(7)=c}}}
Therefore, the center: (h,k)=(-3,-1) 
Foci: (h,k+c), (h,k-c)=(-3,{{{-1+sqrt(7)}}}), (-3,{{{-1-sqrt(7)}}})
Vertices: (h,k+a), (h,k-a)=(-3,-1+4),(-3,-1-4)==>(-3,3),(-3,-5)
Happy Calculating!!!!