Question 31795
Standard equation of ellipse is:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1 where (h,k) is the center, a=1/2(length of one axis), and b=1/2(length of another axis); 
We know that (h,k) = (-4,-5)
So, the equation boils down to
(x+4)^2/a^2 + (y+5)^2/b^2 = 1;
Vertex is at (2,-5) and center is at (-4,-5). This says that the major axis is parallel to x-axis (because y-value for both of them is the same) and 1/2 of the length of the major axis 6 [6 comes from 2-(-4); difference of x-value between vertex and the center]
So, a=6 and b=3 (6/2=3)
Thus, the equation of the ellipse is
(x+4)^2/6^2 + (y+5)^2/3^2 = 1
=>(x+4)^2/36 + (y+5)^2/9 = 1
Correct answer is B.