JEE Main 2026 Mathematics question
Let H : x²/a² − y²/b² = 1 be a hyperbola such that the distance between its foci is 6 and the distance between its directrices is 8/3. If the line x=α intersects the hyperbola H at the points A and B such that the area of the triangle AOB is 4√15, where O is the origin, then α² equals
Answer: (B)
Solution
c=3, and 2a/e = 8/3 gives a²=c²e²·(1/e²)... solving directly: a²=4, b²=5. Area condition: α²·5(α²/4−1)=240 gives α⁴−4α²−192=0, so α²=16.