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Question
Find the equation for the ellipse that satisfies the given conditions:
Vertices (±6, 0), foci (±4, 0)
Solution
Vertices (±6, 0), foci (±4, 0)
Here, the vertices are on the x-axis.
Therefore, the equation of the ellipse will be of the form `x^2/a^2 + y^2/b^2` = 1, where a is the semi-major axis.
Accordingly, a = 6 and c = 4
It is known that a2 = b2 + c2
∴ 62 = b2 + 42
= 36 = b2 + 16
= b2 = 36 - 16
= b = `sqrt20`
Thus, the equation of the ellipse is `x^2/6^2 + y^2/(sqrt(20))^2 = 1` or `x^2/36 + y^2/20 = 1`.
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