Explanation

(c)
Given curves are $y^{2} = x$ and $x^{2} = y$
On differentiating w.r.t. $x,$ we get
$2y\frac{dy}{dx} = 1\$and $2x = \frac{dy}{dx}$
$\Rightarrow \ \ \ \frac{dy}{dx} = \frac{1}{2y}$and $\frac{dy}{dx} = 2x$
At (0,0)
$m_{1} = \frac{dy}{dx} = \infty$ ad $m_{2} = \frac{dy}{dx} = 0$
$\therefore\ \ \ \ \ tan\theta = \frac{m_{2} - m_{1}}{1 + m_{1}m_{2}} = \infty$
$\Rightarrow \ \ \ \ \ \ \theta = \frac{\pi}{2}$