Find the point of intersections of the two circles.

Question

The circles (x+1)^2+(y-1)^2=9 and (x-3)^2+(y+1)^2 are overlapped.

Answer 1

write those as

(x+1)^2 + (y-1)^2 = 3^2, with center at (-1,1) and radius 3

the other equation

(x-3)^2 + (y+1)^2 = r^2 has center of (3,-1) and unknown radius r

the line through the two centers has slope = -2/4 = -1/2

the perpendicular line has slope 2 and goes through the midpoint between the

2 centers = (1,0) half the sum of each of the x and y coordinates.

the equation of the perpendicular line is

y = 2(x-1) = 2x -2

y= 2x -2

find where that perpendicular line crosses either of the two circles. you'll get 2 points generally, or no points, or one point of tangency. two points of intersection, if the circles are overlapping.

if radius = 3 for both equations, the two points of intersection are (1.88, 1.76) and (0.12, -1.76) rounded off to two decimal places.