Let the point be (x1,y1). ∴y12=x1.........(i) y2=x 2y
dy
dx
=1⇒
dy
dx
=
1
2y
∴ Slope of normal at (x1,y1)=
−1
(
dy
dx
)(x1,y1)
=
−1
(
1
2y1
)
=−2y1 It is given that, −2y1=x1....(ii) From Eqs. (i) and (ii), we have y12=−2y1⇒y12+2y1=0 ⇒y1(y1+2)=0⇒y1=0,−2 ∴x1=0,4 Required points are (0,0),(4,−2).