# If the curve $x^2 + 2y^2 = 2$ intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is : Option: 1 $\frac{\pi}{2}+\tan ^{-1}\frac{1}{3}$ Option: 2 $\frac{\pi}{2}-\tan ^{-1}\frac{1}{3}$ Option: 3 $\frac{\pi}{2}-\tan ^{-1}\frac{1}{4}$ Option: 4 $\frac{\pi}{2}+\tan ^{-1}\frac{1}{4}$

Given equation of the curves are

$\\x^2+2y^2=2\\x+y=1$

Homogenising above two equation

$\\x^{2}+2 y^{2}-2(x+y)^{2}=0\\x^2+2y^2-2x^2-2y^2-4xy=0\\-x^2-4xy=0\\x(x+4y)=0\\\Rightarrow x=0\;\;or\;\;x+4y=0$

These are the equation of the line

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

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