Question:
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 :
Correct Option: , 4
Solution:
Homogenising
$x^{2}+2 y^{2}-2(x+y)^{2}=0$
$\Rightarrow-x^{2}-4 x y=0 \Rightarrow x^{2}+4 x y=0$
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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