A) \[\frac{1}{\sqrt{2}}\]
B) \[\frac{1}{2}\]
C) \[\frac{1}{4}\]
D) \[\frac{1}{\sqrt{3}}\]
Correct Answer: A
Solution :
\[\angle FBF'=90{}^\circ \] \[\Rightarrow \] \[\angle OBF'=45{}^\circ \] \[\Rightarrow \] \[ae=b\] and \[{{e}^{2}}=1-\frac{{{b}^{2}}}{{{a}^{2}}}\] \[\Rightarrow \] \[{{e}^{2}}=1-\frac{{{e}^{2}}{{a}^{2}}}{{{a}^{2}}}\] \[\Rightarrow \] \[{{e}^{2}}=1-{{e}^{2}}\] \[\Rightarrow \] \[2{{e}^{2}}=1\] \[\Rightarrow \] \[e=\frac{1}{\sqrt{2}}\]You need to login to perform this action.
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