SOLUTION: x^2/9+(y+3)^2/25=1 whats its center, length of major axis, length of minor axis,foci, and vetexes?

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Question 981057: x^2/9+(y+3)^2/25=1
whats its center, length of major axis, length of minor axis,foci, and vetexes?

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2F9%2B%28y%2B3%29%5E2%2F25=1.....if you compare it to the standard formula of an ellipse ,+%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1, you see that:
h=0
k=-3
so, the center is at (0,-3)
you also see that we have vertical major axis
a%5E2=25=>a=5 and a=-5
b%5E2=9=>b=3 and b=-3
so,
semi-major axis length is a=5
semi-minor axis length isb=+3
find foci:
first we need c
c%5E2=5%5E2-3%5E2
c%5E2=25-9
c%5E2=16
c=4 and c=-4


so, foci will be at (0,-3%2Bc) and (0,-3-c)
(0, -3%2B4) => (0,+1)
and
(0, -3-4) => (0,+-7)
The vertices are at the intersection of the major axis and the ellipse.
vertices are at (0,+-8) and (0,+2)

eccentricity c%2Fa=+4%2F5+=+0.8