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

Physics

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