AP EAMCET · Maths · Parabola
If the focus of a parabola divides a focal chord of the parabola into segments of lengths 5,3 units, then the length of the latusrectum of that parabola is
- A \(\frac{15}{4}\)
- B 20
- C \(\frac{25}{2}\)
- D \(\frac{15}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{15}{2}\)
Step-by-step Solution
Detailed explanation
Since, semi latusrectum is the harmonic mean of segments. So, semi laturectum length \(=\frac{2 \times 5 \times 3}{5+3}=\frac{30}{8}=\frac{15}{4}\) \(\therefore \quad\) Length of latusrectum \(=2 \times \frac{15}{4}=\frac{15}{2}\)
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