1.1. A curve $C$ has equation $y=\text{f}(x)$, where

$\text{f}(x)=\frac{1}{\sqrt{x}},x>0$

The point $P$ lies on $C$ such that the normal to $C$ at $P$ passes through the origin $O$.

Find the coordinates of $P$, giving your answer in the form $({2}^{a},{2}^{b})$, where $a$ and $b$ are rational constants to be found.

1.2. Write down the equation of the normal to $C$ at $P$.

1.3. Show that an equation of the tangent to $C$ at $P$ is

$({2}^{\frac{1}{3}})x+({2}^{\frac{5}{6}})y=3$