The locus of point of trisections of the focal chord of the parabola , `y^2 = 4x` is :

Explanation

`R_x=(2l_1^2+l_2^2)/3`

`P_y=(4l_1+2t_2)/3`

`3x=2t_1^2+t_2^2,3y=2(2t_1+t_2)`

`(9y^2)/4-3x=4t_1^2-4`

`4t_1^2=(9y^2)/4-3x+4`

`t_1^2=9/16*y^2-3/4x+1`

`3x=9/16y^2-3/4x+1+1/(9/16y^2-3/4x+1)`

Complex.