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If x 2 + y 2 = a 2 and x 2 16 + y 2 9 = 1 intersect at 4 points P , Q , R and S which form a square, then the area (in sq. units) of the square is

Options

  1. A144 25
  2. B25 4
  3. C15 2
  4. D576 25

Correct answer

D. 576 25

Step-by-step solution

Let, P = a cos ⁡ θ , a sin ⁡ θ Then, a cos ⁡ θ , a sin ⁡ θ lies on x 2 16 + y 2 9 = 1 Also, θ = 45 ° because P , Q , R , S form a square ⇒ a 2 2 × 16 + a 2 2 × 9 = 1 ⇒ a 2 2 16 + 9 16 × 9 = 1 ⇒ a 2 = 2 × 144 25 ⇒ a = 12 2 5 ⇒ P Q = 24 5 Hence, the area of the square = 576 25

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