Question

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

• 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
$x^2+2y^2-2(x+y{)}^2=0$
$\Rightarrow -x^2-4xy=0$
$\Rightarrow x^2+4xy=0$
Lines are $x=0$ and $y=-\frac{x}{4}$
$\therefore$ Angle between lines
$=\frac{\pi }{2}+{\tan }^{-1}\frac{1}{4}$