A) \[9\]
B) \[\frac{9}{2}\]
C) \[\frac{5}{4}\]
D) \[2\]
Correct Answer: B
Solution :
Given, \[2a=8\] and \[2ac=10\] \[\Rightarrow \] \[e=\frac{10}{8}=\frac{5}{4}\] Now, \[{{b}^{2}}={{a}^{2}}({{e}^{2}}-1)=16\left( \frac{25}{16}-1 \right)=9\] \[\Rightarrow \] \[b=\pm 3\] Hence, length of latuserectum \[=\frac{2{{b}^{2}}}{a}=\frac{2\times 9}{4}\] \[=\frac{9}{2}\]
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