SOLUTION: Write an equation of the ellipse with foci at (0,+-12), and vertices at (0,+-13)

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Question 869588: Write an equation of the ellipse with foci at (0,+-12), and vertices at (0,+-13)
Answer by lwsshak3(11628) About Me  (Show Source):
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Write an equation of the ellipse with foci at (0,+-12), and vertices at (0,+-13)
Given data shows ellipse has a vertical major axis with center at the origin.
Its standard form of equation: x%5E2%2Fb%5E2%2By%5E2%2Fa%5E2=1, a>b
For given ellipse:
a=13 (distance from center to vertices on the vertical major axis)
a^2=169
c=12 (distance from center to foci on the vertical major axis)
c^2=144
c^2=a^2-b^2
b^2=a^2-c^2=169-144=25
b=5
equation of given ellipse: x%5E2%2F25%2By%5E2%2F169=1