Question

The centres of the circle passing through the points (0, 0), (1, 0) and touching the circle x² + y² = 9 are (1/2,±√2).

Answer 1

 Family of circles passing through two points is 

 

Now since the circle touches internally 

[∵ (0, 0), & (1, 0) lie inside the circle]

∴r₁ – r₂ = distance between their centres