### if the cord joining the points t1 and t2 to the parabola y^2 =4ax is normal to the parabola at t1 then prove that t1(t1+t2)=-2

The given parabola is y^2 = 4ax.

The equation of the normal at any point (at^2, 2at) on the parabola is y = -tx + 2at + at^3.

The equation of the chord joining the points t1 and t2 on the parabola is y = a(t1 + t2)x - at1t2.

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