Question

The acute angle between the curves $x y=2$ and $y^{2}=4 x$ at their point of intersection is

• A. $\tan ^{-1} \frac{1}{3}$
• B. $\tan ^{-1} 3$
• C. $\tan ^{-1} 2$
• D. $\tan ^{-1} \frac{2}{3}$

Answer 1

Answer: (B)

$xy = 2 ....$ (1)
and $y^2 = 4x ....$(2)
$x\frac{dy}{dx} + y = 0$
$2y \frac{dy}{dx} = 4$
solving (1) and (2) we get $x =1$ and $y =2$
therefore $m _{1}=-2 \,\,\,m _{2}=1$
$\tan \theta=\left|\frac{m_{1}-m_{2}}{1+m_{1} m_{2}}\right|=\left|\frac{-2-1}{1+(-2)(1)}\right|=3 $
The angle is $\tan ^{-1} 3$