Consider a family of circles which are passing through the point (– 1, 1) and are tangent to x-axis. If (h, k) are the coordinates of the centre of the circles, then the set of values of k is given by the interval

Equation of the circle with centre (h, k) and touching x-axis is                  (x−h)2+(y−k)2=k2   which passes through (– 1, 1)    if              h2+2h−2k+2=0or if        (h+1)2=2k−1For real values of h,2k−1≥0.⇒       k≥1/2