# Proving that this $(X,Y)$ is not uniformly distributed over the unit disk

I'm told that $X$ has uniform distribution on $(-1,1)$ and given $X=x$, $Y$ is uniformly distributed on $(-\sqrt{1-x^2},\sqrt{1-x^2})$. I know it's not uniformly distributed over the unit disk $\{(x,y):x^2+y^2\lt 1\}$, because my professor did this in class but I didn't quite understand what he was talking about. For a reason why, it was because I was just a few minutes late for class and he doesn't like to explain things twice. So could anyone show how he did this?

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