question_answer

The equations of lines through the point \[(1,\,1)\] and making angles of \[{{45}^{o}}\]with the line \[x+y=0\]are

A)  \[x-1=0,\,\,x-y=0\]

B)  \[x-1=0,\,\,y-1=0\]

C)  \[x-y=0,\,\,y-1=0\]

D)  \[x+y-2=0,\,\,\,y-1=0\]

Correct Answer: B

Solution :

Since, the required lines make an angle \[{{45}^{o}}\] either above the line or below the line. \[\therefore \] Required slopes are \[m={{90}^{o}},\,{{180}^{o}}.\] \[\therefore \]\[(y-1)=\tan \,{{90}^{o}}(x-1)\] \[\Rightarrow \]\[x=1\] and \[(y-1)=\tan \,{{180}^{o}}(x-1)\Rightarrow y=1\]