# Joint density of $(R,X)$ when $(X,Y)$ is uniform on the unit circle and $R^2=X^2+Y^2$

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 $$t
She claimed that it is resulted from the constraints $$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