Geo2.8

Find the equation of a straight line joining the points $(at_1^2,2at_1),(at_2^2,2at_2)\,$

The equation of the required line is

$y-2at_1=\frac{2at_2-2at_1}{a(t_2+t_1)(t_2-t_1)}\cdot(x-at_1^2)\,$

Simplifying

$y-2at_1=\frac{2}{t_2+t_1}\cdot(x-at_1^2)\,$

$(t_1+t_2)(y-2at_1)=2(x-at_1^2)\,$

$2x-(t_1+t_2)y+2at_1t_2=0\,$