Question

If the endpoint t₁, t₂ of a chord satisfy the relation t₁t₂ = k (const.) then prove that the chord always passes through a fixed point. Find the point?

Answer 1

Equation of chord joining (at₁² , 2at₁) and (at₂² , 2at₂) is

∴ This line passes through a fixed point (– ak, 0)