Question

The coordinates of the ends of a focal chord of a parabola y² = 4ax are (x₁ , y₁) and (x₂ , y₂) then value of x₁ x₂ + y₁ y₂ is equal to

a. 3a²

b. – 3a²

c. a²

d. – a²

Answer 1

Correct option is b. – 3a²

: Let(at₁² ,2at₁) ≡ (x₁ , y₁) and (at₂² ,2at₂) ≡ (x₂, y₂) such that t₁ t₂ = –1

∴x₁ x₂ + y₁ y₂ = a² t² t²₂ + 4a² t₁ t₂ = a² – 4a² = –3a²