Given curve is y2=4x .........(i) Let the equation of line by y=mx+c Since
dy
dx
=m=1 and this line is passing through the point (0,1). ∴1=1(0)+c⇒c=1 ∴y=x+1 .......(ii) Solving Eqs. (i) and (ii), we get (x+1)2=4x ⇒(x−1)2=0 ⇒x=1and y=2 This shows that line touch the curve at one point. So length of intercept is zero.