The graph shows two circles:
(x-1)² + (y-1)² = 1 and (x-2)² + (y-2)² = 2
There are two points of intersection: A and B.
Use the slider, p, to change the second circle.
Make p smaller until the circles intersect at A = (1,2) and B = (2,1)
(1) What is the equation of the circle now?
(2) Show by substitution in the circles' equations that A and B actually lie on both circles.
Dave Mulkey, Created with GeoGebra