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If a point P 0 , - 2 and Q is any point on the circle, x 2 + y 2 - 5 x - y + 5 = 0 , then the maximum value of P Q 2 is

Options

  1. A8 + 5 3
  2. B47 + 10 6 2
  3. C14 + 5 3
  4. D25 + 6 2

Correct answer

C. 14 + 5 3

Step-by-step solution

Given circle x 2 + y 2 - 5 x - y + 5 = 0 ⇒ x - 5 2 2 + y - 1 2 2 = 3 2 On circle Q = ( 5 2 + 3 2 cos θ , 1 2 + 3 2 sin θ ) P Q 2 = 5 2 + 3 2 cos ⁡ θ​ 2 + 5 2 + 3 2 sin ⁡ θ​ 2 P Q 2 = 25 2 + 3 2 + 5 3 2 cos θ​ + sin θ​ = 14 + 5 3 2 cos ⁡ θ​ + sin ⁡ θ​ ∴ Maximum value of P Q 2 = 14 + 5 3 2 2 = 14 + 5 3 .

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