Why is this a beta distribution?

Question

I'm given a circle with point $A$ defined by $(x,y)$. Then $T=1-d[O,A]$, so $T=1-\sqrt{(x^2+y^2)}$.

Asked to find:

1. $P[T<=u]$
2. $E[T]$
3. $Var(T)$

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Alright, so $d[O,A]$ has the CDF $u^2$. So, for the first piece, $P[T<=u]=1-u^2$.

However, our professor has given us also the hint that $u^2$ is beta-distributed. For $Y$ that follows a beta distribution,

$$E[Y]=\frac{a}{a+b}$$ $$Var(Y)=\frac{ab}{(a+b)^2(a+b+1)}$$

So I kind of know what the answers are supposed to be, aside from the fact that I don't see how $u^2$ follows a beta distribution, so I don't know what the values $a$ and $b$ would be.

Ultimately, I think the generalized answers are:

2. $$E[T]=E[1-Y]=E[1]-E[Y]=1-\frac{a}{a+b}$$

3. $$Var(T)=Var(1-Y)=Var(T)=\frac{ab}{(a+b)^2(a+b+a)}$$

   Help uncovering the beta distribution parameters would be greatly appreciated. Thank you!