The elimination of θ from x cos θ - y sin θ = 2 and x sin θ + y cos θ = 4 will give:

$3x^2 - y^2 = 20$ $x^2 + y^2 = 20$ $3x^2 + y^2 = 20$ $x^2 - y^2 = 20$

$x^2 + y^2 = 20$

x cos θ - y sin θ = 2 On squaring both sides x² cos²θ + y² sin²θ - 2xy sinθ cosθ  = 4      ---------(1) And, x sin θ + y cos θ = 4  x² sin²θ + y² cos²θ + 2xy sinθ cosθ  = 16      ------(2) On adding 1 and 2 , x² ( cos²θ+ sin²θ ) + y² ( sin²θ + cos²θ) = 4 + 16 = 20 x² + y² = 20