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Question
Find the equation for the ellipse that satisfies the given conditions:
Vertices (0, ±13), foci (0, ±5)
Solution
Vertices (0, ±13), foci (0, ±5)
Here, the vertices are on the y-axis.
Therefore, the equation of the ellipse will be of the form `x^2/b^2 + y^2/a^2` = 1, where a is the semi-major axis.
Accordingly, a = 13 and c = 5
It is known that a2 = b2 + c2
∴ 132 = b2 + 52
= 169 = b2 + 25
= b2 = 169 - 25
= b = `sqrt144` = 12
Thus, the equation of the ellipse is `x^2/12^2 + y^2/13^2 = 1` or `x^2/144 + y^2/169 = 1`.
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