find the points of intersection of parabola and the circle
y=1+2x-x^2
x^2-2x+y^2=3
Please show step by step
(1) $\displaystyle y = 1 + 2x - x^2$
(2) $\displaystyle 3 = x^2 - 2x + y^2$.
Add the equations together to eliminate the $\displaystyle x$ terms.
$\displaystyle y + 3 = 1 + y^2$
$\displaystyle 0 = y^2 - y -2$
$\displaystyle 0 = (y - 2)(y + 1)$
$\displaystyle y = 2$ or $\displaystyle y = -1$.
Substitute these values into equation (1) and solve for $\displaystyle x$.