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If b and c are the lengths of the segments of any focal chord of a parabola yΛ2 = 4ax , then length of semi latus rectum is - ?

If b and c are the lengths of the segments of any focal chord of a parabola yΛ2 = 4ax , then length of semi latus rectum is - ?

Grade:11

1 Answers

Arun
25763 Points
2 years ago

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)

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