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

2 answers

x^2 + y^2 - 10x - 8y + 18 = 0
x^2-10x + y^2-8y = -18
x^2-10x+25 + y^2-8y+16 = -18+25+16
(x-5)^2 + (y-4)^2 = 23

The second equation has a typo. Fix it and complete the squares to find its center.

Then compare the distance between centers to the sum of the radii.
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