Explanation

(d)
The smallest circle means that its radial is, distance from origin to the diameter is smallest.
[image:11_image67.emf]
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.
Alternate It is clear from the figure that centre lies on IInd quadrant.
Hence, option (d) is correct