Question

If the curves, x² – 6x + y² + 8 = 0 and x² – 8y + y² + 16 – k = 0, (k > 0) touch each other at a point, then the largest value of k is ______.

Answer 1

Common tangent is S₁ – S₂ = 0

Answer 2

Two circle touches each other if C₁C₂ = |r₁ ± r₂| Distance between C₂ (3, 0) and C₁ (0,4) is either √k + 1 or |√k - 1| (C₁C₂ = 5)

⇒ √k + 1 = 5 or |√k - 1| = 5

⇒ 16 or k = 36