Weibull & Exponential distribution

$\displaystyle X$ is a random variable with weibull distribution given with

$\displaystyle

f(x;\alpha ,\beta) = \begin{cases}

\frac{\alpha}{\beta^\alpha}x^{\alpha-1}e^{-(x/\beta)^{\alpha}} & x>0\\

0 & x=0\end{cases}

$

Let $\displaystyle \alpha=2$ and $\displaystyle Y=2X^2/\beta^2$.

Show that $\displaystyle Y$ has exponential distribution and find value of parameter $\displaystyle \lambda$.

I believe that $\displaystyle G(Y)=P(Y \leq y)$ should be expressed in terms of $\displaystyle X$ , but I don't know where to start.