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so lets say i want to determine the coordinates of intersection of these two circles so lets just uh very quickly visualize whats going on here weve got the x minus 3 squared plus y plus 8 squared so its got a center of 3 minus 8 with a radius of 10. okay so just a very quick diagram whats going on so 3 minus 8 somewhere down here its the center radius of ten something like that maybe okay and then youve got um this other circle x plus 2 squared plus y minus 3 squared equals 121. so center at minus 2 3 so further along a bit up not too much more and and radius of 11. so a little bit larger i dont know something like that okay so weve got these two circles anyway they dont need to be accurate im not interested in where they cross the x and y axis the point is that they intersect at two distinct points and i want to find the coordinates of these so what i could do first is i could expand both of these circle equations to get x squared minus 6x plus 9 plus y squared plus 16 y