Question

If the curve $x^{2}+2 y^{2}=2$ 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

• A. $\frac{\pi}{2}+\tan ^{-1}\left(\frac{1}{3}\right)$
• B. $\frac{\pi}{2}-\tan ^{-1}\left(\frac{1}{3}\right)$
• C. $\frac{\pi}{2}-\tan ^{-1}\left(\frac{1}{4}\right)$
• D. $\frac{\pi}{2}+\tan ^{-1}\left(\frac{1}{4}\right)$

Answer 1

Answer: (D)

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
$=\frac{\pi}{2}+\tan ^{-1} \frac{1}{4}$