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)

Sol. Circle

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.