Tangents drawn to parabola y² = 4ax at the points A and B intersect at C then,

$$\begin{gathered} Given parabola y^2=4ax \\ focus S=(a,0) \\ Let A=(a{t_1}^2,2a{t}_1),B=(a{t_2}^2,2a{t}_2) be two points on parabola \\ Tangents drawn at A and B intersect at C \\ then C=(a{t}_1{t}_2,a(t_1+t_2\left)\right) \\ Now abscissa of A,C,B are a{t_1}^2,a{t}_1{t}_2,a{t_2}^2 are in G.P \\ and ordinates of A,C,B are 2a{t}_1,a(t_1+t_2),2a{t}_2 are in A.P. \end{gathered}$$