A) \[\frac{1}{\sqrt{3}}\]
B) \[\frac{1}{4}\]
C) \[\frac{1}{2}\]
D) \[\frac{1}{\sqrt{2}}\]
Correct Answer: D
Solution :
Since, \[\angle FBF'={{90}^{o}},\]then \[\angle OBF'={{45}^{o}}\]and \[\angle BF'O={{45}^{o}}\] \[\Rightarrow \] \[ae=b\] (\[\because \Delta \Beta OF'\]is an isosceles triangle) and \[{{e}^{2}}=1-\frac{{{b}^{2}}}{{{a}^{2}}}\] \[\Rightarrow \] \[{{e}^{2}}=1-\frac{{{a}^{2}}{{e}^{2}}}{{{a}^{2}}}\Rightarrow {{e}^{2}}=1-{{e}^{2}}\] \[\Rightarrow \] \[2{{e}^{2}}=1\Rightarrow e=\frac{1}{\sqrt{2}}\] (\[\because e\]cannot be negative)You need to login to perform this action.
You will be redirected in
3 sec