The angle between the curves ${\mathrm{x}}^2=4\mathrm{y}, {\mathrm{y}}^2=4\mathrm{x}$ at (4, 4) is

$\begin{array}{l}{y}^2=4x\\ 2y\frac{dy}{dx}=4\\ \frac{dy}{dx}=\frac{2}{y}\\ m_1={\left(\frac{dy}{dx}\right)}_{(4,4)}=\frac{1}{2}\end{array}$
$\begin{array}{l}{x}^2=4y\\ 2x=4\frac{dy}{dx}\\ \frac{dy}{dx}=\frac{x}{2}\\ m_2={\left(\frac{dy}{dx}\right)}_{(4,4)}=2\\ \mathrm{Tan}\theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|\\ =\left|\frac{\frac{1}{2}-2}{1+1}\right|=\frac{3}{4}\\ \theta ={\mathrm{Tan}}^{-1}\left(\frac{3}{4}\right)\end{array}$