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Question
Find the equation for the ellipse that satisfies the given conditions:
Ends of major axis (0, `+- sqrt5`), ends of minor axis (±1, 0)
Sum
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Solution
Ends of major axis `(0, ±sqrt5)`, ends of minor axis (±1, 0)
Here, the major axis is along 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 = sqrt5` and b = 1.
Thus, the equation of the ellipse is `x^2/1^2 + y^2/(sqrt5)^2 = 1` or `x^2/1 + y^2/5 = 1`.
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