Question

The locus of the point of intersection of tangents drawn at the extremities of the focal chord of a parabola x² = 4a(y+a) is

• A. y+a =0
• B. y – a= 0
• C. y+2a = 0
• D. y – 2a = 0

Answer 1

Answer: (C)

y+2a = 0

Answer 2

(x₁, y₁) be the point of the intersection of tangents drawn at the extremities of the focal chord then the equation of focal chord is S₁ = 0.

xx₁ – 2a(y+y₁) = 4a²

but this passes through the focus (0, 0)

⇒ 0.x₁ – 2a(0+y₁) = 4a²

∴ The locus of (x₁, y₁) is y+2a =0