Question

 If the normal at the point t₁ on the parabola y² = 4ax meets it again at point t₂ then prove that t₁t₂ + t₁² + 2 = 0. 

Answer 1

Equation of the parabola is y² = 4ax 

Equation of normal at t₁= (at₁² ,2at₁ ) is 

y+xt₁ = 2at₁+ at₁³ . 

This normal meets the parabola again at (at₂² ,2at₂ ) . 

Therefore,