Mathematics - Parabola Question with Solution | TestHub

Let $t_1,t_2\&t_3$ be the conormal points drawn from $\left(x_1,y_1\right)$ to $y^2=4ax$ Equation of the normal at point 't' to $y^2=4ax$ is $y+tx=2at+a{t}^3$ This passes through $\left(x_1,y_1\right)\Rightarrow y_1+t{x}_1=2at+a{t}^3\Rightarrow a{t}^3+\left(2a-x_1\right)t-y_1=0$ $t_1,t_2,t_3$ are the roots of the equation. $\therefore t_1+t_2+t_3=0$ The ordinate of the centroid of the triangle formed by the points $t_1,t_2\&t_3$ is $\frac{2a}{3}\left(t_1+t_2+t_3\right)=0$