Tangent 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 coordinates of ‘P’ so that area of triangle PP1P2 is minimum, is

OP=52sec⁡θ,OA=52cos⁡esθ Area of ΔPAB=100sin⁡2θIf area is min is max of sin 2θ θ=π/4⇒OP=10

Tangent 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 coordinates of ‘P’ so that area of triangle PP1P2 is minimum, is

OP=52sec⁡θ,OA=52cos⁡esθ Area of ΔPAB=100sin⁡2θIf area is min is max of sin 2θ θ=π/4⇒OP=10

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Tangent 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 coordinates of ‘P’ so that area of triangle PP₁P₂ is minimum, is

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(10, 0)

$(10 \sqrt{2}, 0)$

(–10, 0)

$(- 10 \sqrt{2}, 0)$

answer is A, C.

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Detailed Solution

$OP = 5 \sqrt{2} \sec θ, OA = 5 \sqrt{2} \cos e s θ$
$Area of ΔPAB = \frac{100}{\sin 2 θ}$
If area is min is

max of sin $2 θ$

$θ = π / 4 \Rightarrow OP = 10$

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Tangent 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 coordinates of ‘P’ so that area of triangle PP1P2 is minimum, is

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Tangent 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 coordinates of ‘P’ so that area of triangle PP₁P₂ is minimum, is