JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
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:
- A \( \pi-\tan^{-1}(\frac{1}{4}) \)
- B \( \frac{\pi}{2}+\tan^{-1}(\frac{1}{4}) \)
- C \( \frac{\pi}{2}+2\tan^{-1}(\frac{1}{4}) \)
- D \( \frac{\pi}{2}-\tan^{-1}(\frac{1}{4}) \)
Answer & Solution
Correct Answer
(B) \( \frac{\pi}{2}+\tan^{-1}(\frac{1}{4}) \)
Step-by-step Solution
Detailed explanation
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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