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
x2y2=4
B
x2+y2=2
C
xy=3
D
x2+y2=3

Solution

## 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 BPhysics

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