If the curve


If the curve $x^{2}+2 y^{2}=2$ intersects the line $\mathrm{x}+\mathrm{y}=1$ at two points $\mathrm{P}$ and $\mathrm{Q}$, then the angle subtended by the line segment PQ at the origin is :

  1. $\frac{\pi}{2}+\tan ^{-1}\left(\frac{1}{3}\right)$

  2. $\frac{\pi}{2}-\tan ^{-1}\left(\frac{1}{3}\right)$

  3. $\frac{\pi}{2}-\tan ^{-1}\left(\frac{1}{4}\right)$

  4. $\frac{\pi}{2}+\tan ^{-1}\left(\frac{1}{4}\right)$

Correct Option: , 4



$x^{2}+2 y^{2}-2(x+y)^{2}=0$

$\Rightarrow-x^{2}-4 x y=0 \Rightarrow x^{2}+4 x y=0$

Lines are $x=0$ and $y=-\frac{x}{4}$

$\therefore$ Angle between lines $=\frac{\pi}{2}+\tan ^{-1} \frac{1}{4}$

option (4)

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