The curve whose subtangent is n times the abscissa of the point of contact and passes through$(2, 3)$ represent

According to the given condition 

$\begin{array}{l}\frac{y}{f^{\mathrm{\prime }}\left(x\right)}=nx\\ y\frac{dx}{dy}=nx\Rightarrow \frac{dy}{y}=\frac{1}{n}\frac{dx}{x}\end{array}$

Integrating $y^n=Cx$ This passes through $(2,3)$ if $3^n/2=C$ 

So $y^n=\frac{3^{n}x}{2}$

$\Rightarrow {\left(\frac{y}{3}\right)}^n=\frac{x}{2}.$For $n=2$ This represents a parabola whose axes coincide with x-axis