Question

If P₁Q₁ & P₂Q₂ or are two focal chords of y² = 4ax then the chord P₁P₂& Q₁Q₂ intersect on

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

Answer 1

Answer: (B)

Directrix

Answer 2

Let co-ordinates of points are

P₁ (at₁², 2at₁), P₂ (at₂², 2at₂), Q₁ $\left( \frac{a}{{t_{1}}^{2}},\frac{- 2a}{t_{1}} \right)$

Q₂$\left( \frac{a}{t_{2}^{2}},\frac{–2a}{t_{2}} \right)$

\ equation of P₁P₂ is

(t₁ + t₂) y = 2 (x + at₁t₂) ……(i)

equation of Q₁ Q₂ is

(t₁ + t₂) y + 2 (x t₁ t₂ + a) = 0 …..(ii)

Solving (i) & (ii)

x = –a