Question

If b and c are lengths of the segments of any focal chord of the parabola y²=4ax, then what is the length of latus-rectum

Answer 1

We know that, the semi latus-rectum of a parabola is the harmonic mean between the segments of any focal chord of the parabola.

Given that, b and c are lengths of the segments of any focal chord of the parabola y²=4ax

So, Let l is the length of semi-latus rectum of the parabola. 

Then,1/b+1/c=2/l

⇒ l=2bc/(b+c)

Hence, length of latus-rectum=2bc/(b+c)