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If b and c are the lengths of the segmen...

If b and c are the lengths of the segments of any focal chord of a parabola `y^(2)=4ax` , then length of the semi-latus rectum is:

A

`(b+c)/(2)`

B

`(bc)/(b+c)`

C

`(2bc)/(b+c)`

D

`sqrt(bc)`

Text Solution

Verified by Experts

The correct Answer is:
C

Let `P(at_(1)^(2), 2at_(1)) and Q (at_(2)^(2), 2at_(2))` are end points of a chord
PQ is a focal chord
`t_(1)t_(2)= -1`
`t_(2)= (-1)/(t_(1))`
`Q((a)/(t_(1)^(2)), (-2a)/(t_(1)))`
`b=SP=PM=a+at_(1)^(2)`
`b-a=at_(1)^(2) ...........(i)`
`c= SQ=QN=a+(a)/(t_(1)^(2))`
`c-a=(a)/(t_(1)^(2)) ...........(ii)`
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