Question

Examine if the two circles x² + y² – 2x – 4y = 0 and x² + y² – 8y – 4 = 0 touch each other externally or internally.

Answer 1

Given circles are x² + y² – 2x – 4y = 0 ...........(i) 

and x² + y² – 8y – 4 = 0 ...........(ii) 

Let A and B be the centres and r₁ and r₂ the radii of circles (i) and (ii) respectively, then 

A ≡ (1, 2), B ≡ (0, 4), r₁ = √5, r₂ = 2√5

Thus AB = |r₁ – r₂|, hence the two circles touch each other internally.