Question

Which of the following equations gives a circle?

• A. $r=2\sin \theta$
• B. $r^2\cos 2\theta =1$
• C. $r(4\cos \theta +5\sin \theta )=3$
• D. $5=r(1+\sqrt{2}\cos \theta )$

Answer 1

Answer: (A)

Now, taking option (a)
i.e. $r=2\sin \theta$
Let $x=r\sin \theta ,$
$y=r\cos \theta$
$\Rightarrow r^2=2r\sin \theta$
$\Rightarrow x^2+y^2=2y$
$\left[\because x^2+y^2=r^2\right]$
This equation represents a circle.