SOLUTION: show analytically that the circles x(squared) + y(squared) - 6x + 4=0 and x(squared) + y(squared) - 2x + 8y + 12=0 are tangent to each other.

Question 24545: show analytically that the circles x(squared) + y(squared) - 6x + 4=0 and x(squared) + y(squared) - 2x + 8y + 12=0 are tangent to each other.
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
well, if the 2 circles are tangents, it means they just touch. This would mean that the length of the line joining their centres will equal their 2 radii added.

So, that is the plan...find the centres and radii lengths and then prove that the length between the 2 centres is equal to the radii added together.

so, centre is (3,0) and radius is .

so centre is (1,-4) and radius is .

So, now for the proof:
Distance between 2 centres is found using Coordinate Geometry:
distance =
distance =
distance =
distance =
distance =
distance =
distance =
distance =

And radii added together are which is also ... so proved :-)

jon.

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