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

- x
^{2}+y^{2}=a^{2}+b^{2} - x
^{2}/y^{2}+a^{2}/b^{2}=1 - x
^{2}¸y^{2}=a^{2}-b^{2} - x
^{2}/a^{2}+ y^{2}/b^{2}=1

**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