Question

If the coordinates of a variable point $P$ be $(\cos \theta +\sin \theta ,\sin \theta -\cos \theta )$, where $\theta$ is the parameter, then the locus of $P$ is

• A. $x^2-y^2=4$
• B. $x^2+y^2=2$
• C. $xy=3$
• D. $x^2+y^2=3$

Answer 1

The correct option is B $x^2+y^2=2$

$x=\cos \theta +\sin \theta y=\sin \theta -\cos \theta \Rightarrow x^2+y^2={(\cos \theta +\sin \theta )}^2+{(\sin \theta -\cos \theta )}^2\Rightarrow x^2+y^2={\sin }^2\theta +{\cos }^2\theta -2\sin \theta \cos \theta +{\sin }^2\theta +{\cos }^2\theta +2\sin \theta \cos \theta \Rightarrow x^2+y^2=2$

Correct option is B