Shortest distance lie along the normal Slope of normal at A is ( −t )⇒(−t)=t2−a2t−0⇒t=0t2=a−2t2−a=−2(t2−a)2+(2t)2=16⇒t2=3,a=5Equation of circle passing through (1,0) and (5,0) and having centre on the axis will be diametric form(x−1)(x−5)+y⋅y=0x2+y2−6x+5=0