The coordinates of the center of the smallest circle passing through the origin and having $y = x + 1$ as a diameter are

Question

$\left(-\frac{1}{2}, \frac{1}{2}\right)$

$\left(\frac{1}{2}, -\frac{1}{2}\right)$

$\left(\frac{1}{2}, \frac{1}{2\sqrt{3}}\right)$

$(-1, 0)$

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