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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