5. The gradient at any point \(( x , y )\) on a curve is proportional to \(\sqrt { y }\).
Given that the curve passes through the point with coordinates \(( 0,4 )\),
- show that the equation of the curve can be written in the form
$$2 \sqrt { y } = k x + 4$$
where \(k\) is a positive constant.
Given also that the curve passes through the point with coordinates ( 2,9 ),
- find the equation of the curve in the form \(y = \mathrm { f } ( x )\).
5. continued