Find the intersection points for the circles:
(x+2)^2+(y-3)^2=25
and
(x-1)^2+(y+4)^2=16
you can brute-force your way into this in several ways. For example,
(x+2)^2 + (y-3)^2 = (x-1)^2 + (y+4)^2 + 9
x^2+4x+4 + y^2-6y+9 = x^2-2x+1 + y^2+8y+16 + 9
4x+4 - 6y+9 = -2x+1 + 8y+25
6x - 14y = 13
Now, using 6x+12 = 14y+25
x+2 = (14y+25)/6
((14y+25)/6)^2 + (y-3)^2 = 25
y = (-121±3√1311)/116
so, x = (-31±7√1311)/116
Or, you can work with the line joining the centers, as in this example:
https://stackoverflow.com/questions/3349125/circle-circle-intersection-points