The equation r cos (θ-(π)/3 )=2 represents

Correct answer: (D) a straight line. Hint: r cos (θ-(π)/3 )=2 ⇒ r cos θ × 1/2+r sin θ × (√3)/2=2 ⇒ x+√3 y=4(x=r cos θ, y=r sin θ) ∴ a straight line

Q73 / 155 · WBJEE 2020 · Mathematics

The equation $r \cos \left(\theta-\frac{\pi}{3}\right)=2$ represents

A
a circle
B
a parabola
C
an ellipse
Correct answer
D
a straight line

Solution

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

Hence, the correct answer is option: 'D'.

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