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Question
Eliminate θ from the following :
x = 4cosθ − 5sinθ, y = 4sinθ + 5cosθ
Solution
x = 4cosθ − 5sinθ ...(i)
y = 4sinθ + 5cosθ ...(ii)
Squaring (i) and (ii) and adding, we get
x2 + y2 = (4cos θ – 5sin θ)2 + (4sin θ + 5cos θ)2
= 16 cos2θ – 40sinθ cosθ + 25 sin2θ + 16 sin2θ + 40sinθ cosθ + 25 cos2θ
= 16(sin2θ + cos2θ) + 25(sin2θ + cos2θ)
= 16(1) + 25(1)
= 41
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