Conic Sections - Ellipse Help

Hey, I'm still kind of confused as to how to do this for this type of ellipse. If I see it done, than I'll probably be able to understand it better, thanks!

(Standard) Equation: [(x-9)^2/25] + [(y+2)^2/100] = 1

What's the center (9,-2), the foci, the major and minor axises, and the vertices of this ellipse?

Thanks again!

[(x - 9)² / 25] + [(y + 2)² / 100] = 1

Center (9, - 2)

Since the larger denominator is on the y side of the equation, the major axis will be parallel to the y axis ('a' is always the larger value), so

a² = 100
b² = 25

a = √(a²)
a = √100
a = ± 10

b = √(b²)
b = √25
b = ± 5

y-axis vertices will be 'a' units above and below the center, so

y = - 2 + 10
y = 8

and

y = - 2 - 10
y = - 12

y vertices (9, 8) & (9, - 12)
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x vertices will be 'b' units to the left and right of center, so

x = 9 + 5
x = 14

and

x = 9 - 5
x = 4

x vertices (14, - 2) & (4, - 2)
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The foci are 'c' units above and below center, and

        ______
c = √ a² - b²
        _______
c = √100 - 25
        ___
c = √ 75

c = ± 8.66

Focus (9 , k ± 8.66), so

Focus (9, - 2 + 8.66)
Focus (9, 6.66)

and

Focus (9, - 2 - 8.66)
Focus (9, - 10.66)

Focii (9, 6.66) & (9, - 10.66)
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