Question

If α₁, α₂ are the lengths of segments of a focal chord of a parabola, then its latusrectum is

• A. $\frac{2\alpha_{1}\alpha_{2}}{\alpha_{1} + \alpha_{2}}$
• B. $\frac{\alpha_{1}\alpha_{2}}{\alpha_{1} + \alpha_{2}}$
• C. $\frac{4\alpha_{1}\alpha_{2}}{\alpha_{1} + \alpha_{2}}$
• D. α₁ + α₂

Answer 1

Answer: (C)

$\frac{4\alpha_{1}\alpha_{2}}{\alpha_{1} + \alpha_{2}}$

Answer 2

We know that $\frac{1}{SP} + \frac{1}{SQ} = \frac{2}{\mathcal{l}}$

⇒ $\frac{1}{\alpha_{1}} + \frac{1}{\alpha_{2}} = \frac{2}{\mathcal{l}}$

⇒ $2\mathcal{l}\mspace{6mu} = \mspace{6mu}\frac{4\alpha_{1}\alpha_{2}}{\alpha_{1} + \alpha_{2}}$ = length of latusrectum.