1.1. A curve is described by the equation $y=f(x)$, where

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

P is the point on the curve such that the normal to the curve at P also passes through the origin.

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

1.2. Write down the equation of the normal to the curve at P.

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

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