Question

On the parabola y² = 8x, if one extremity of a focal chord is (½, -2), then its other extremity is

• A. (4, 4)
• B. (4, -4)
• C. (8, -8)
• D. (8, 8)

Answer 1

Answer: (D)

(8, 8)

Answer 2

Let (1/2, -2) = ($at_{1}^{2},\mspace{6mu} 2at_{1})$

⇒ t₁= -1/2

If ‘t₂’ is the other extremity of the focal chord t₁.t₂ = -1, t₂ = -1/t₁ = 2

∴ The other extremity = $\left( at_{2}^{2},2at_{2} \right)$ = (8, 8)