Given, y=f(x) Equation of tangent of curve y=f(x) at P(α,1) is y−1=f(α)(x−α) Equation of normal of curve at P(α,1) is y−1=−‌
1
f′(α)
(x−a) ∴ Tangent cut of X -axis at A ∴A=(α−‌
1
f′α
,0) ∴Normal cut of X -axis at B ∴‌‌B=(α+f′(α),0 Point ‌‌C=(α,0) AC+BC=α−α+‌
1
f′(α)
+α+f′(α)−α AC−BC=‌
1
f′(α)
+f′(α) AC+BC is minimum When, ‌‌f′(α)=1 ∴ Equation of tangent ofcurve y−1=1(x−α)⇒x−y=α+1 ∴ Equation of tangent of curve is parallel to x−y=0