Question

1. If b and c are lengths of the segments of any focal chord of the parabola y²=4ax, then write the length of its latus-rectum.

Answer 1

$$\begin{gathered} \text{We know that, the semi latus-rectum of a parabola is the harmonic mean between} \\ \text{the segments of any focal chord of the parabola.} \\ {\text{Given that, b and c are length of the segments of any focal chord of the parabola y}}^2\text{=4ax} \\ \text{So,} \\ \text{Let l is the length of semi latus-rectum of the parabola. Then,} \\ \frac{1}{b}+\frac{1}{c}=\frac{2}{l} \\ \Rightarrow l=\frac{2bc}{b+c} \\ \text{Hence, length of latus-rectum=}\frac{2bc}{b+c} \end{gathered}$$