Find an equation of an ellipse satisfying the given conditions.

Foci: (-1,6) and (-1,0); Length of major axis: 10

Need more of a check on my answer. If it's wrong, then I'll need some explanations on how to do the problem. If right, then that's all I really need.

The center is obviously the midpoint between the 2 Foci, so it's (-1,3) and it's vertical.

So it's equation is:

(x+1)^2/b^2 + (y-3)^2/a^2 = 1

A is half the length of the major axis (10) so a would = 5.

A squared = 25

C is x in the foci, so it's 1.

C squared = 1

So to find b^2, I need to plug values into:

C^2 = a^2 - b^2

1=25-b^2

b^2 = 24

So, assuming all of the above is correct, the final equation should be:

(x+1)^2/24 + (y-3)^2/25 = 1

Correct? Thanks.