Tangents are drawn to the circle x^2 + y^2 = 50 from a point ‘P’ lying on the x-axis…

Problem: Tangents are drawn to the circle $x^2 + y^2 = 50 $ from a point ‘P’ lying on the x-axis. These tangents meet the y-axis at points P₁ and P₂. Possible coordinates of ‘ P ‘ so that area of triangle PP₁P₂ is minimum is / are

(A) (10, 0)

(B) (10√2 , 0)

(C) (-10, 0)

(D) (-10√2 , 0)

Ans: (A) & (C)

Sol: Solution : OP = 5√2 secθ ,

OP₁ = 5√2 cosecθ

Δ PP₁P₂ = 100/sin2θ

(Δ PP₁P₂)_min = 100

⇒ θ = π/4 ⇒ OP =10

⇒ P=(10, 0), (–10, 0)

Hence (A) and (C) are the correct answers.