Question

Suppose AB is a focal chord of the parabola \( y^2 = 12x \) of length \( l \) and slope \( m<\sqrt{3} \). If the distance of the chord AB from the origin is \( d \), then \( ld^2 \) is equal to _________.

Answer 1

Correct Answer: 108

For a focal chord of the parabola \(y^2 = 12x\), we have:

\[ l = 4a \csc^2 \theta \]

Given that \(l = 12x\) and using the property of a focal chord, we find:

\[ l = 12 \times \frac{9}{d^2} \]

Thus:

\[ l d^2 = 108 \]