If x = 8(sinθ + cosθ) and y = 9(sinθ - cosθ), then the value of x^28^2 + y^29^2 is:

Answer: Option D

$$\begin{array}{rl}& \frac{x}{8}=\sin \theta +\cos \theta ........\left(\text{i}\right)\\ & \frac{y}{9}=\sin \theta -\cos \theta ........\left(\text{ii}\right)\\ & \text{Square and add equation}\left(\text{i}\right)\text{and}\left(\text{ii}\right)\\ & \frac{x^2}{8^2}+\frac{y^2}{9^2}={\sin }^2\theta +{\cos }^2\theta +2\sin \theta \cos \theta +{\sin }^2\theta +{\cos }^2\theta -2\sin \theta \cos \theta \\ & \frac{x^2}{8^2}+\frac{y^2}{9^2}=2\end{array}$$