Equation of the chord joining any two points on the parabola

From the straight line chapter we know: "The equation of a line having slope m and passing through (x1,y1) is

(y-y1) = m(x-x1)"

slope between (x1,y1) and (x2,y2) = (y2-y1)/(x2-x1)

Two points on parabola are A(at1²,2at1) and B(at2²,2at2)

So the equation joining these two points is

(y-2at1) = [(2at2-2at1)/(at2²-at1²)]*(x-at1²)
=> y - 2at1 = [2/(t2+ta)]*(x-at1²)
=> y(t1+t2) = 2x+2at1t2