show that the circles x^2 + y^2 - 10x - 8y + 18 = 0 and x^2 + y^2 - 8y - 4y + 14 = 0 do not intersect

are you ever going to fix the typo? Why keep wasting time with the same flawed posting?

x^2 + y^2 - 8y - 4y + 14 = 0