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Question

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

A
b+c2
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B
bcb+c
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C
2bcb+c
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D
bc
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Solution

## The correct option is A 2bcb+cWe 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=4axSo, Let l is the length of semi-latus rectum of the parabola. Then,1b+1c=2l⇒l=2bcb+cHence, length of semi-latus-rectum=2bcb+c

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