Equation of circle whose centre is (h,k) and touch the x -axis i.e (x−h)2+(y−k)2=k2
(radius of circle =k because circle is tangent to x -axis) ∵ Equation of circle passing through (-1,1) ∴(−1−h)2+(1−k)2=k2 ⇒1+h2+2h+1+k2−2k=k2 ⇒h2+2h−2k+2=0 D≥0 ∴(2)2−4×1⋅(−2k+2)≥0