EllipseMedium
Question
Let the line $y - x = 1$ intersect the ellipse $\frac{x^{2}}{2} + \frac{y^{2}}{1} = 1$ at the points A and B . Then the angle made by the line segment AB at the center of the ellipse is :
Options
A.$\pi - \tan^{- 1}\left( \frac{1}{4} \right)$
B.$\frac{\pi}{2} + \tan^{- 1}\left( \frac{1}{4} \right)$
C.$\frac{\pi}{2} + 2\tan^{- 1}\left( \frac{1}{4} \right)$
D.$\frac{\pi}{2} - \tan^{- 1}\left( \frac{1}{4} \right)$
Solution
By solving line & equation of ellipse we get $x = 0$ & $x = - \frac{4}{3}$
$${\therefore B\left( - \frac{4}{3}, - \frac{1}{3} \right) }{m_{OB} = tan\theta = \frac{1}{4} }{\because\angle AOB = \frac{\pi}{2} + \theta = \frac{\pi}{2} + \tan^{- 1}\frac{1}{4}}$$
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