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, $
$y=r \cos \theta$
$\Rightarrow r^{2}=2 r \sin \theta$
$\Rightarrow x^{2}+y^{2}=2 y $
$\left[\because x^{2}+y^{2}=r^{2}\right]$
This equation represents a circle.