A) \[\left( \frac{1}{2},\frac{-1}{2} \right)\]
B) \[\left( \frac{1}{2},\frac{1}{3} \right)\]
C) \[(-1,0)\]
D) \[\left( -\frac{1}{2},\frac{1}{2} \right)\]
Correct Answer: D
Solution :
The smallest circle means that is radial is, distance from origin to the diameter id smaller. Let equation of line perpendicular to \[y-x=1\] is \[x+y=\lambda \] Also, it passes through \[(0,0)\]. \[\therefore \] \[\lambda =0\] \[\therefore \] Perpendicular line is \[x+y=0.\] The intersection point of lines are \[\left( -\frac{1}{2},\frac{1}{2} \right)\] Which is the centre of circle.You need to login to perform this action.
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