how to apply implicit function in derivatives I find this question rather akwardly put.... have a look 

The tangent to the curve: $y^2 - x^3$ passes point $P(1,1)$ and cuts the axes at points $Q$ and $R$ for $x$- and $y$-axis respectively. Find the ration $\overline{PR} : \overline{RQ}$.

I am unable to interprete this implicitly,

can we interprete as $f(x, y) = y^2 - x ^3$  of $y^2 - x^3 = 0?$
$y^2 -x^3 = 0 \Leftrightarrow \frac{d}{dx}(y^2) = \frac{d}{dx}(x^3) \Leftrightarrow 2y\frac{dy}{dx} = 3x^2 \Leftrightarrow \frac{dy}{dx} = \frac{3x^2}{2y}$
This is how implicit differentiation is done, however it's not needed for your case. You may explicitly find $y(x) = x^{3/2}$ and solve the problem using formula for tangent line.
$y^2 -x^3 = 0 \Leftrightarrow \frac{d}{dx}(y^2) = \frac{d}{dx}(x^3) \Leftrightarrow 2y\frac{dy}{dx} = 3x^2 \Leftrightarrow \frac{dy}{dx} = \frac{3x^2}{2y}$
This is how implicit differentiation is done, however it's not needed for your case. You may explicitly find $y(x) = x^{3/2}$ and solve the problem using formula for tangent line.