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Member warned that homework must be posted in one of the Homework sections

**Mentor note**: Moved from a technical math section.

What is the proof that the family of circles out of two non-intersecting circles, no two circles in that family intersect.

Say S1 = x^2 + y^2 - 8x + 7 = 0 (i.e center at (4,0) and radius = 3 )

S2 = x^2 + y^2 - 24x + 135 = 0 ( i.e center at (12,0) and radius = 3 )

Family of circles of the two above circles is S1 + k S2 = 0.

i.e x^2 + y^2 + [2* (-4 -12k)/(1+k)] x + [ (7 + 135k ) / (1+k) ] = 0 , k ∈ R

Thanks.

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