Question

If P₁Q₁ and P₂Q₂ are two focal chords of parabola y² = 4ax then the chords P₁ P₂ and Q₁Q₂ intersect on the-

• A. Axis
• B. Tangent at vertex
• C. Directrix
• D. None

Answer 1

Answer: (C)

Directrix

Answer 2

Let coordinate of P₁, P₂, Q₁, Q₂ be P₁(at₁², 2at₁), P₂(at₂²,2at₂) and Q₁(a/t₁²,–2a/t₁), Q₂(a/t₂², –2a/t₂)

\ Equation of P₁P₂ is

(t₁ + t₂)y = 2(x + at₁t₂) .....(1)

and equation of Q₁Q₂ is

y(t₁ + t₂) + 2(xt₁t₂ + a) = 0 .....(2)

Solving (1) and (2)

x + a = 0 which is directrix.