The question is like this:

A point $(X,Y)$ is picked at random uniformly in the unit circle.
Find the joint density of $R$ and $X$, where $R^2 = X^2 + Y^2$.

The TA drew a diagram like this and claim that
$F_{R,X}(r,t)=r^2$ when $t>r$ and $F_{R,X}(r,t)=0$ when $t<r$
She claimed that it is resulted from the constraints $x^2+y^2 \le r^2 $ and $x\le t$
But I don't understand why it is like this, isn't it we can always find $y$ whenever there is a $x$, why would $t$ matters? Can anyone please explain, thank you so much enter image description here


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