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MathsJEE Main 23 Jan 2026, Shift 1·Q5·MCQ·Moderate

Conic Sections · Ellipse and line intersection

Let the line y−x=1y - x = 1 intersect the ellipse x22+y21=1\dfrac{x^2}{2} + \dfrac{y^2}{1} = 1 at the points AA and BB. Then the angle made by the line segment ABAB at the center of the ellipse is:
  1. (1)π−tan⁡−1(14)\pi - \tan^{-1}\left(\dfrac14\right)
  2. (2)π2+tan⁡−1(14)\dfrac{\pi}{2} + \tan^{-1}\left(\dfrac14\right)
  3. (3)π2+2tan⁡−1(14)\dfrac{\pi}{2} + 2\tan^{-1}\left(\dfrac14\right)
  4. (4)π2−tan⁡−1(14)\dfrac{\pi}{2} - \tan^{-1}\left(\dfrac14\right)

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