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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

The line segment joining A 5 , 0 and B 10 cos ⁡ θ , 10 sin ⁡ θ is divided internally in the ratio 2 : 3 at P . If θ varies, then the perimeter of locus of P is

Options

  1. A4 π units
  2. B16 π units
  3. C8 π units
  4. D6 π units

Correct answer

C. 8 π units

Step-by-step solution

Let P h , k be the point dividing te line segment in the ratio 2 : 3 , then h = 2 10 cos ⁡ θ + 3 5 2 + 3 = 4 cos ⁡ θ + 3 and k = 2 10 sin ⁡ θ + 3 0 2 + 3 = 4 sin ⁡ θ ∴ h - 3 2 + k 2 = 16 ⇒ Locus of P h , k is x - 3 2 + y 2 = 16 , which is a circle. Hence, the perimeter of the circle is 2 π 4 = 8 π units

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