A circle passes through the points A (1, 0), B (5, 0) and touches the y-axis at C (0, h). if ∠ACB is maximum then

Equation of any circle passing through (1, 0) and (5, 0) is y2+(x−1)(x−5)+λy=0 i.e. x2+y2+λy−6x+5=0 If ∠ACB is maximum, then this circle must touch the y-axis at (0, h). Putting x=0 in the equation of circle, we gety2+λy+5=0 . It should have y=h as it is a repeated root.⇒h2=5 and λ=−2h ⇒|h|=5