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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
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Verified Answer
The correct answer is:
$\frac{9}{2}$
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 $=\frac{2 b^2}{a}=\frac{2 \times 9}{4}=\frac{9}{2}$
$$
2 a e=10 \text { and } 2 a=8
$$
$$
a e=5, a=4
$$
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 $=\frac{2 b^2}{a}=\frac{2 \times 9}{4}=\frac{9}{2}$
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