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AP EAMCET · Maths · Hyperbola

If in a hyperbola, the distance between the foci is 10 and transverse axis has length 8, then the length of its latus rectum is

  1. A 9
  2. B \(\frac{9}{2}\)
  3. C \(\frac{32}{3}\)
  4. D \(\frac{64}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{9}{2}\)

Step-by-step Solution

Detailed explanation

Given, \[ 2 a e=10 \text { and } 2 a=8 \] \[ a e=5, a=4 \] In hyperbola, \[ \begin{aligned} & & (a e)^2 & =a^2+b^2 \\ \Rightarrow & & 25 & =16+b^2 \\ \Rightarrow & & b^2 & =9 \end{aligned} \] Length of latus rectum \(=\frac{2 b^2}{a}=\frac{2 \times 9}{4}=\frac{9}{2}\)