# Thread: parabola and circle

1. ## parabola and circle

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

2. Originally Posted by skml02
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) $y = 1 + 2x - x^2$

(2) $3 = x^2 - 2x + y^2$.

Add the equations together to eliminate the $x$ terms.

$y + 3 = 1 + y^2$

$0 = y^2 - y -2$

$0 = (y - 2)(y + 1)$

$y = 2$ or $y = -1$.

Substitute these values into equation (1) and solve for $x$.