If x=a sin θ – b cos θ, y=cos θ + b sin θ, then Which of the Following is True?

  1.  x2+y2 =a2+b2
  2. x2/y2 +a2/b2 =1
  3. x2 ¸y2 =a2-b2
  4. x2/a2 + y2/b2=1
Anurag Mishra Professor Asked on 26th October 2015 in Maths.
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  • 1 Answer(s)

    first option is correct

    Explanation:-

    x = a sinθ – b cosθ and y = a cos θ + b sin θ

    Then, x² + y² = (a sinθ – b cos θ)² + (a cos θ + b sinθ)²
    = (a² sin²θ + b² cos²θ – 2 ab sinθ cosθ) + (a² cos²θ + b² sin²θ + 2 ab sinθcosθ)
    = a² sin²θ + b² cos²θ + a² cos²θ + b² sin²θ – 2 ab sinθ cosθ+ 2 ab sinθ cosθ
    = a² (sin²θ + cos²θ) + b² (sin²θ + cos²θ)
    = a²+ b²
    x² + y² =a²+ b²

    Then, the first option is (1)x² + y² =a²+ b²

    Hence, the answer is (1) x² + y² =a²+ b²

    Monis Rasool Professor Answered on 28th October 2015.
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