Question 141

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

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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