A) \[\frac{3}{\sqrt{2}}\]
B) \[\sqrt{3}\]
C) \[3\sqrt{2}\]
D) \[2\sqrt{3}\]
Correct Answer: C
Solution :
[c] \[2ae=6\] \[\frac{2a}{e}=12\] Multiplying both; \[4{{a}^{2}}=72\] \[{{a}^{2}}=18\] \[\Rightarrow e=\frac{6}{2.3\sqrt{2}}=\frac{1}{\sqrt{2}}\] \[{{e}^{2}}=1-\frac{{{b}^{2}}}{{{a}^{2}}}=\frac{1}{2}\] \[\frac{18}{2}={{b}^{2}}\Rightarrow {{b}^{2}}=9\] \[\therefore \] Latus rectum \[=\frac{2{{b}^{2}}}{a}=\frac{2\times 9}{3\sqrt{2}}=\frac{6}{\sqrt{2}}=3\sqrt{2}\]
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