Question

The length of the focal chord of a parabola which is inclined at 30⁰ is-

• A. 8a
• B. 12a
• C. 16a
• D. 8$\sqrt{3}$a

Answer 1

Answer: (C)

16a

Answer 2

Let parabola is y² = 4ax

Q PQ is a focal chord

Q slope of PQ

̃ $\frac{\left( - \frac{2a}{t} - 2at \right)}{\left( \frac{a}{t^{2}} - at^{2} \right)}$ = tan 30⁰

̃ $\frac{- 2a\left( \frac{1}{t} + t \right)}{a\left( \frac{1}{t} + t \right)\left( \frac{1}{t} - t \right)}$

= $\frac{1}{\sqrt{3}}$̃$\left( t - \frac{1}{t} \right)$=2$\sqrt{3}$

\focal chord (PQ) = a $\left( t + \frac{1}{t} \right)^{2}$

= a $\left\{ \left( t - \frac{1}{t} \right)^{2} + 4 \right\}$= a {(2$\sqrt{3}$)² + 4} = 16a