Question

The angle between the curves $xy=2$ and $y^2=4x$ is

Answer 1

$xy=2,y^2=4x$

Angle between two corners means angle b/w their tangents

$y+x\frac{dy}{dx}=0$

$m_1=\frac{dy}{dx}=\frac{-y}{x}$

$2y\frac{dy}{dx}=4$

$m_2=\frac{dy}{dx}=\frac{2}{y}$

$Q=\left|\frac{m_1-m_2}{1+m_2{m}_1}\right|=\left|\frac{\frac{2}{y}+\frac{y}{x}}{1-\frac{2}{x}}\right|$

$=\frac{y^2+2x}{y(x-2)}$