The elimination of θ from x cosθ - y sinθ = 2 and x sinθ + y cosθ = 4 will give?

Answer: Option A

$$\begin{array}{rl}& xsin\theta +y\cos \theta =4\\ & \underline{x\cos \theta -y\sin \theta =2}\left[\text{Formula}\right]\\ & \left(x^2+y^2\right)\left(\text{co}{\text{s}}^2\theta +{\sin }^2\theta \right)=4^2+2^2\\ & \Rightarrow x^2+y^2=a^2+b^2\\ & \Rightarrow \left(x^2+y^2\right)\left(1\right)=16+4\\ & \Rightarrow x^2+y^2=20\end{array}$$