If circle and and parabola have maximum number of common chord then least integral value of  is

(5)

For maximum number of common chord, circle and parabola must intersect in 4 distinct points

Let us first find the value of  when circle and parabola touch each other

For that solving the given curves we have or

Curves touch if discriminant  or

Hence least integral value of  for which the curves intersect is 5