The minimum distance between the curves y = tan ⁡ x ,   ∀ x ∈ - π 2 , π 2 and x - 2 - π 4 2 + y 2 = 1 is

Step-by-step solution

The minimum distance between two curves lies along their common normal. Let, P h , t a n h lies on y = tan ⁡ x Then, the equation of normal at P is y - tan ⁡ h = - 1 s e c 2 h x - h this passes through the centre of the circle, hence, tan ⁡ h sec 2 ⁡ h = 2 + π 4 - h ⇒ h = π 4 Minimum distance = distance between π 4 , 1 and 2 + π 4 , 0 - 1 = 5 - 1