Im having some trouble figuring out how I know a function is homothetic.

I have this CES utility function which represents homothetic preferences:

$\displaystyle u(x_1,x_2)=(x_1^{-p}+x_2^{-p})^{\frac{\--1}{p}}$

I know that it is homogeneous of degree 1,

$\displaystyle u(tx_1,tx_2)=t^1(x_1^{-p}+x_2^{-p})^{\frac{\--1}{p}}$

but is that by definition enough to conclude that it is homothetic?

Help would be much appreciated..