Solution
Expression 1 : $$xcos \theta - ysin \theta = 2$$
Squaring both sides :
=> $$x^2cos^2 \theta + y^2sin^2 \theta - 2xy sin \theta cos \theta = 4$$
Similarly, squaring expression 2, we get :
=> $$x^2sin^2 \theta + y^2cos^2 \theta + 2xy sin \theta cos \theta = 16$$
Adding above equations,
=> $$x^2 (cos^2 \theta + sin^2 \theta) + y^2 (cos^2 \theta + sin^2 \theta) = 20$$
=> $$x^2 + y^2 = 20$$
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