If the midpoint of a chord of the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\) is \((\sqrt{2}, \frac{4}{3})\), and the length of the chord is \(\frac{2 \sqrt{\alpha}}{3}\), then \(\alpha\) is :

[JEE Main 2025, 28 Jan (Shift 2)]

Question

If the midpoint of a chord of the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\) is \((\sqrt{2}, \frac{4}{3})\), and the length of the chord is \(\frac{2 \sqrt{\alpha}}{3}\), then \(\alpha\) is :

[JEE Main 2025, 28 Jan (Shift 2)]

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If the midpoint of a chord of the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\) is \((\sqrt{2}, \frac{4}{3})\), and the leng…

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