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

A. x² + y² = 20

B. 3x² + y² = 20

C. x² - y² = 20

D. 3x² - y² = 10

Answer: Option A

Solution(By Examveda Team)

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