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If the tangents P Q and P R are drawn from a variable point P to the ellipse x 2 16 + y 2 9 = 1 , such that the fourth point S of the parallelogram P Q S R lies on the circumcircle of the Δ P Q R , then the area (in sq. units) of the locus of P is

Options

  1. A7 π
  2. B16 π
  3. C25 π
  4. D9 π

Correct answer

C. 25 π

Step-by-step solution

Parallelogram P Q S R is a cyclic quadrilateral ⇒ Parallelogram is a rectangle ⇒ ∠ Q P R = 90 o Let, the equation of the tangent from P h , k to the ellipse is y = m x ± 16 m 2 + 9 ⇒ k - m h 2 = 16 m 2 + 9 ∵ m 1 m 2 = - 1 ⇒ h 2 - 16 = - k 2 + 9 ⇒ locus of P is x 2 + y 2 = 25 Hence, the area of locus of P is 25 π sq. units

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