Since $\rho = \large\frac{PM}{RT}$ (where $M$ is the molecular mass of the gas),

Since it's given that $\large\frac{p^2}{\rho} = $ constant, it follows that $\large\frac{p^2}{\frac{PM}{RT}} =$ constant.

$\Rightarrow PT = $ constant.

$\Rightarrow$ the graph is a hyperbola.