The two parabolas  $y^2=4x\text{ and }{x}^2=4y$  intersect at a point $P$, whose abscissae is not zero, such that

$y^2=4x\to \left(1\right);x^2=4y\to \left(2\right)$

Solving  (1) & (2):  ${\left(\frac{x^2}{4}\right)}^2=4x\Rightarrow x^3=4^3\Rightarrow x=4\therefore P(4,4)$

Slope of the tangents to $y^2=4x\text{ at }P\text{ is }{m}_1=1/2$

Slope of the tangents to $x^2=4y\cdot \text{ at }P\text{ is }{m}_2=2$

$m_1{m}_2=1/2\times 2=1\Rightarrow \text{ Tangents at }P$ make complementary angles with x-axis.