Verified answer

With the foci points along the y-axis, right away you know the equation will be in the form of:

(x - h)^2/b^2 + (y - k)^2/a^2 = 1

First, the easy stuff. The center is at (0,0), the center point of the foci. So h=0 and k=0.

Also, a is the distance from the center to either vertex, so a = 6

And, c is the distance from the center to either focus. c = 3√3

Now the fun stuff: We need to find b by using the relation c^2 = a^2 - b^2

Solving for b,

-b^2 = c^2 - a^2

b^2 = a^2 - c^2

b = √(a^2 - c^2)

b = √(6^2 - (3√3)^2)

b = √(36 - 27)

b = √9

b = +/- 3

So that makes the equation

x^2/9 + y^2/36 = 1

The foci are equivalent distances from the midsection (the area is c) and the vertices are equivalent distances from the midsection on the comparable axis (the area is a). The x is fastened at -2 so the axis is vertical; halfway between a million and 5 is 3. So the midsection is (-2,3). C could be 2. The vertices are 8 aside, so A=4. B^2 =A^2 -C^2 so B^2 =4^2 -2^2 =12. The axis is vertical so the A^2 is under the y. (x+2)^2/12 +(y-3)^2/sixteen =a million.