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प्रश्न
Find the equation for the ellipse that satisfies the given condition:
Vertices (±5, 0), foci (±4, 0)
उत्तर
Vertices (±5, 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 = 5 and c = 4
It is known that a2 = b2 + c2
∴ 52 = b2 + 42
= 25 = b2 + 16
= b2 = 25 - 16
= b = `sqrt9` = 3
Thus, the equation of the ellipse is `x^2/5^2 + y^2/3^2 = 1` or `x^2/25 + y^2/9 = 1`.
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