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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
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:
Solution
By solving line & equation of ellipse we get $x = 0$ and $x = -\frac{4}{3}$
$\therefore B\left(-\frac{4}{3}, -\frac{1}{3}\right)$
$m_{OB} = \tan\theta = \frac{1}{4}$
$\therefore \angle AOB = \frac{\pi}{2} + \theta = \frac{\pi}{2} + \tan^{-1}\left(\frac{1}{4}\right)$
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