Multiple choice

The locus of the middle point of the chord of the circle $x^2 + y^2 = 1$ such that the segment of the chord on the parabola $y = x^2 - x$ subtends a right angle at the origin, is a circle whose centre and radius respectively are

  1. (1, 1) and $\sqrt {2}$

  2. (1, 1) and 2
  3. $(\frac {1}{2}, \frac {1}{2})$ and $\frac {1}{2}$
  4. $(\frac {1}{2} ,\frac {1}{2})$ and $\frac {1}{\sqrt {2}}$
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