show that the circle x square + y square=2 and x square + y square - 6 x minus 6 y + 10 = 0 touch each other do the circles touch externally or internally also find their point of contact
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The equation of circles are X2+y2-4x-6y-12=0 and X2+y2+6x+18y+26=0
centres are C1(2,3),C2(-3,-9)
R1=√4+9+12=5
R2=√9+81-26=8
C1,C2=√(2+3)2+(3+9)2
√25+144
13=r1+r2
Therefore, circles touch e externally.
Equation of common tangent is s1-s2=0
-10x-24y-38=0
5x+12y+19=0
The point of contact p divides C1,C2 in the ratio of 5:8
coordinates of p:(5(-3)+8.2\5+8,6(-9)+8.3/5+8)=1/13,-21/3
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