Q. Which of the following equations gives circle?
A) $r = 2\sin\theta$
B) $r^{2}{cos\ }{2\theta} = 1$
C) $r\left( 4\cos\theta + 5\sin\theta \right) = 3$
D) $5 = r(1 + \sqrt{2}\cos\theta)$
Explanation
(a)
Now, taking option $(a)$
$r = 2\sin\theta$
Let $x = r\cos\theta,\ \ \ y = r\sin\theta$
$\therefore\ \ \ r^{2} = 2r\sin\theta$
$\Rightarrow \ \ \ x^{2} + y^{2} = 2y$
Which represents a equation of circle
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.