圓形comman tangent

http://pstock.idv.tw/files-pstock/9031605.pdf

算把啦
我摺埋......
k=-1 係comon chord only

Since the lowest point of C1 is ( 2,1) and the lowest point of C2 is ( 6,1), so one of the 2 common tangents is y = 1.
Centre of C1 is (2,4) and centre of C2 is (6,6), so equation of line passing through the 2 centres is:
(y-4)/(6 -4) = (x -2)/(6 -2)
(y-4)/2 = (x-2)/4
2y - 8 = x -2
2y = x + 6.
When y = 1, x = -4, so the line intersects the tangent y = 1 at (-4,1).
Slope of line passing through the 2 centres = (6-4)/(6-2) = 1/2
= tan a where a is the angle between these 2 lines.
Based on the principle of tangent to circle, slope of the other tangent is tan 2a = 2 tan a/(1 - tan^2 a) = 2(1/2)/[1 - (1/2)^2]
= 1/(1 - 1/4) = 4/3.
Since the 2nd tangent also passes through (-4, 1). So equation of the other common tangent is
y - 1 = 4/3(x + 4)
3y - 3 = 4x + 16
3y = 4x + 19.
So the 2 common tangents are : y = 1 and 3y = 4x + 19.

點解 k 要 = -1既???