Question:medium
Let \(H: \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) be a hyperbola such that the distance between its foci is 6 and the distance between its directrices is \(\frac{8}{3}\). If the line \(x = \alpha\) intersects the hyperbola H at the points A and B such that the area of the triangle AOB is \(4\sqrt{15}\), where O is the origin, then \(a^2\) equals:
Let \(H: \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) be a hyperbola such that the distance between its foci is 6 and the distance between its directrices is \(\frac{8}{3}\). If the line \(x = \alpha\) intersects the hyperbola H at the points A and B such that the area of the triangle AOB is \(4\sqrt{15}\), where O is the origin, then \(a^2\) equals:
Updated On: Apr 10, 2026
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The Correct Option is A
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