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The equation \(r \cos \left(\theta-\frac{\pi}{3}\right)=2\) represents
(A) a circle
(B) a parabola
(C) an ellipse
(D) a straight line

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Ans: (D)
Hint : \(r \cos \left(\theta-\frac{\pi}{3}\right)=2 \quad \Rightarrow r \cos \theta \times \frac{1}{2}+r \sin \theta \times \frac{\sqrt{3}}{2}=2 \Rightarrow x+\sqrt{3} y=4 \quad(x=r \cos \theta, y=r \sin \theta)\)
\(\therefore\) a straight line
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