Straight line $y = x + 2$ cuts circle at $x^{2} + y^{2} = 20$ at $A$ and $B$ determine the values of $A$ and $B$ Im currently studying circles so now that I have two equations I'm confused. I'm asked to determine the values of $A$ and $B$ given straight line $y = x+2$ that cuts circle at $x^{2} + y^{2} = 20$.

If $(x,y)$ is in the intersection of the line $y=x+2$ and the circle $x^2+y^2=20$, then\begin{align*}x^2+(x+2)^2 & =20 \\
x^2+x^2+4x+4 & =20 \\
2x^2+4x-16 & =0 \\
x^2+2x-8 & =0 \\
(x-2)(x+4) & =0
\end{align*}hence $x=2$ or $x=-4$. This gives the points $(2,4)$ and $(-4,-2)$, because $y=x+2$.
