Question

The normals drawn at three points to a parabola y² = 8x are concurrent at (3,4). Then the product of the ordinates of the points is

• A. 1
• B. 2
• C. 4
• D. 128

Answer 1

Answer: (D)

128

Answer 2

Equation of normal to the parabola y+xt = 2at + at³. This passes through (3, 4)

∴ 4+3t = 4t + 2t³

⇒ 2t³ + t – 4 = 0.

∴ t₁. t₂.t₃ = $\frac{- a_{3}}{a_{0}} = \frac{4}{2} = 2$ (product of roots).

∴ $y_{1}.y_{2}.y_{3} = (2at_{1})(2at_{2})(2at_{3})$ = $8.a^{3}.(t_{1}t_{2}t_{3})$

= 8.8.2 = 128