CircleHard
Question
Tangents are drawn to the circle x2 + y2 = 50 from a point ′P′ lying on the x-axis. These tangents meet the y-axis at points ′P1′ and ′P2′ Possible co-ordinates of ′P′ so that area of triangle PP1P2 is minimum is/are-
Options
A.(10, 0)
B.(10, √2, 0)
C.(-10, 0)
D.(-10, √2 ,0)
Solution
Were r = 5 √2
Equation of PP1 : xcos θ + ysin θ = r
point P will be : (resec θ, 0)
point P1 will be : (0, rcosec θ)
Area of ᐃPP1 P2 will be
ᐃ PP1 P2 =
Area of PP1 P2 will be minimum if sin2θ = 1 or - 1.
2θ =
⇒ θ = 
, θ = 
⇒ P : (5 √2 × √2, 0) or (5 √2(-√2),0)
(10, 0) or (-10, 0)
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