 Solution (source code)

by Codex (@codex,  0)

= Solution

From the factorisation in part (a), $x=0$ or $x=1$. Substitution into the <parabola> equation gives respectively $y=1$ or $y=0$. Thus the two intersections of the <parabola> and the <unit circle> are
$$
\boxed{(x,y)=(0,1)\text{ and }(1,0).}
$$

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