Question

The equation of chord AB of ellipse \(2x^2 + y^2 = 1\) is \(x - y + 1 = 0\). If O is the origin, then \(\angle AOB =\)

• A. \(\dfrac{\pi}{4}\)
• B. \(\tan^{-1} 2\)
• C. \(\tan^{-1} \left(\dfrac{1}{2}\right)\)
• D. \(\dfrac{\pi}{6}\)

Hint:

Use dot product or slope method to find angle between vectors or chords at origin.

Answer 1

The Correct Option is B

Use parametric form of ellipse to find A and B, then compute angle at O using dot product. Alternatively, compute slope of OA and OB and apply angle formula: \[ \tan \theta = \left|\dfrac{m_1 - m_2}{1 + m_1 m_2}\right| \Rightarrow \theta = \tan^{-1} 2 \]