• # question_answer If the angle between the lines joining the end points of minor axis of an ellipse with its foci is ${{x}^{2}}-{{y}^{2}}=25$, then the eccentricity of the ellipse is [IIT Screening 1997; Pb. CET 2001; DCE 2002] A)            1/2  B)            $1/\sqrt{2}$ C)            $\sqrt{3}/2$                             D)            $1/2\sqrt{2}$

Correct Answer: B

Solution :

Since $\angle \,FBF'=\frac{\pi }{2}$ (Given) $\therefore$$\angle \,FBC=\,\angle \,F'BC=\pi /4$                      $CB=CF\Rightarrow \,\,b=ae$ Þ ${{b}^{2}}={{a}^{2}}{{e}^{2}}$                   Þ ${{a}^{2}}(1-{{e}^{2}})={{a}^{2}}{{e}^{2}}$            Þ $1-{{e}^{2}}={{e}^{2}}$ Þ $2{{e}^{2}}=1$ Þ $e=1/\sqrt{2}$.

You need to login to perform this action.
You will be redirected in 3 sec