AP EAMCET · Maths · Parabola
If \(b\) and \(c\) are the lengths of the segments of any focal chord of a parabola \(y^2=4 a x\), then the length of the semi-latus rectum is :
- A \(\frac{b c}{b+c}\)
- B \(\sqrt{b c}\)
- C \(\frac{b+c}{2}\)
- D \(\frac{2 b c}{b+c}\)
Answer & Solution
Correct Answer
(D) \(\frac{2 b c}{b+c}\)
Step-by-step Solution
Detailed explanation
Since the semi latus rectum of a parabola is the harmonic mean between the segments of any focal chord of the parabola. \(\therefore l\) is the harmonic mean between \(b\) and \(c\). Hence, \(l=\frac{2 b c}{b+c}\)
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