AP EAMCET · Maths · Parabola
The length of the latus rectum of a parabola whose focal chord \(P S Q\) is such that \(P S=3\) and \(Q S=2\) is
- A \(\frac{24}{5}\)
- B \(\frac{12}{5}\)
- C \(\frac{6}{5}\)
- D \(\frac{12}{10}\)
Answer & Solution
Correct Answer
(A) \(\frac{24}{5}\)
Step-by-step Solution
Detailed explanation
We know that the length of the semi latus rectum is the harmonic mean of focal radii, so length of the latus rectum \[ =2\left(\frac{2(P S)(Q S)}{P S+Q S}\right)=2 \times \frac{2 \times 3 \times 2}{3+2}=\frac{24}{5} \]
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