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      Question

      If 2ycosθ = x sinθ and 2xsecθ – ycosecθ = 3, then

      x 2 + 4y 2 = ?
      A 4 Correct Answer Incorrect Answer
      C 1 Correct Answer Incorrect Answer
      D 2 Correct Answer Incorrect Answer

      Solution

      We have, 2y cosθ = xsinθ and 2xsecθ – y cosecθ =3
      Put θ = 45º , then, 2y/√2 = x/√2
      ⇒2y = x ⇒ 2y – x = 0 …… (1)
      And, 2x√2 – y√2 = 3
      ⇒2x – y = 3/√2………… (2)
      Now, (ii) + 2 (i) we get 2x – y = 3/√2
      –2x + 4y = 03y = 3/√2
      3y = 3/√2 ⇒ y = 1/√2 So, x = 2y = 2 × 1/√2 = 2
      =2 × 1/√2 = 2
      Now, x 2 + 4y 2 ⇒ (√2) 2 + 4 × (1√2) 2 ⇒ 2 + 2 = 4

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