Let (h1,k) be the mid-point of chord of parabola y2=4x. ∴ Equation of chord is yk−2(x+h)=k2−4h [∵ Equation of chord of parabola when mid-point (x, y) is T=S1] ⇒yk−2x−2h=k2−4h...(i) Chord are drawn through vertex ∴h=
x
2
and k=
y
2
⇒2h=x and 2k=y Putting the values of x and y in Eq. (i), we get 2k2−4h−2h=k2−4hk2=2h ∴ Locus of the mid-point of the parabola is y2=2x