Co-ordinate Parabola Circle Contained in it; Difference in maximum and minimum possible radius

Question

If the Difference of radii of larget and smallest Circle passing through the focus of Parabola $$Y^2=4x$$ and toughing parabola in at least one point is My Approach Let Circle be $$C: (x-a)^2+y^2=r^2$$ Since it passes through focus of parabola:(1,0) => $$r^2=(1-a)^2$$ $$C: (x-a)^2+y^2=(1-a)^2$$ Solving for Parabola and Circle; putting $$Y^2=4x$$ in circle equation $$(x-a)^2+4x=(1-a)^2 => x^2+x(4-2a)+2a-1 $$ Since the Circle will touch the parabola at only ONE POINT; the equation's Discriminant = 0 Which gives a=1,5 which gives r=0,4 r=4 is correct but r=0 means point circle which doesn't touches the parabola; where did I go wrong ? and the answer to the question is 7/2