# Thread: need help with circle proof

1. ## need help with circle proof

If two circles x^2 + y^2 + Ax + By + C =0 and x^2 + y^2 + ax + by + c = 0 intersect at two points,
find an equation of the line through their points of intersection.

Also prove that if two circles intersect at two points, then the line through their points of intersection
is perpendicular to the line through the centers of the circles.

2. ## Re: need help with circle proof

you can just try to solve those 2 equations by elimination (taking one to minus the other).

it is also helpful to remember the equation $\displaystyle x^2+y^2+Ax+By+C+k(x^2+y^2+ax+by+c)=0$
when $\displaystyle k=-1$, this is a line passing through the intersection of the circles.
when $\displaystyle k\neq-1$, this is a circle passing through the intersection of the 2 circles.
that's if i remember correctly, and this equation is just used generally. for example if the 2 circles do not intersect no such line will even exist. or if the circles intersect at one point only there is an infinite number of lines that pass through that intersection.
others please correct me if i'm wrong