Question

If the equation $x^2+y^2=2x$ is written in polar coordinate system, then $r$ can be

• A. $0$
• B. $1$
• C. $2\cos \theta$
• D. $2\sin \theta$

Answer 1

Answer: (A), (C)

$2\cos \theta$

Since, we know that
$x=r\cos \theta ,y=r\sin \theta$
Now putting this in the given equation, we have
$x^2+y^2=2x$
$\Rightarrow r^2{\cos }^2\theta +r^2{\sin }^2\theta =2r\cos \theta$
$\Rightarrow r^2({\sin }^2\theta +{\cos }^2\theta )=2r\cos \theta$
$\Rightarrow r^2=2r\cos \theta$
$\Rightarrow r(r-2\cos \theta )=0$
$\Rightarrow r=0$ or $r=2\cos \theta$