The equation of the parabola, y2=4x The equation of the normal to the parabola, y2=4ax at (am2,−2am) is y=mx−2am−am3 Here, a=1, the equation of the normal becomes, y=mx−2m−m3 since the normal is perpendicular to the line, x+3y+1=0 Thus, m1m2=−1 m(
−1
3
)=−1 m=3 Substitute the values in equation (I). y=3x−2(3)−33 y=3x−6−27 3x−y=33